A firefighting crew uses a water cannon that shoots water at 27.0 m/s at a fixed angle of 50.0 ∘ above the horizontal. The firefighters want to direct the water at a blaze that is 12.0 m above ground level. How far from the building should they position their cannon? There are two possibilities (d1Part A: d1=_____m Part B: d2=______m
In projectile motion , range of projectile is given by the expressions
R = u²sin2θ / g
where u is velocity of projectile.
u = 27 m/s θ = 50
12 = 27² sin 2θ / 9.8
sin 2θ = .16
θ = 9.2 / 2
When we place 90- θ in place of θ , in the formula of range , we get the same value of projectile. hence at 85.4 ° , the range will be same.
The Lamborghini Huracan has an initial acceleration of 0.80g. Its mass, with a driver, is 1510 kg. If an 80 kg passenger rode along, what would the car's acceleration be?
The problem discusses the change in acceleration when a passenger is added to a car. It requires understanding of Newton's second law of motion, force equals mass times acceleration, and then recalculating the acceleration with the passenger added to the total mass.
This problem pertains to Newton's second law of motion, stating that the force applied on an object equals its mass times its acceleration (F = ma). Given that the initial acceleration of the Lamborghini Huracan with a driver is 0.80g or 0.80*9.80 m/s², we can calculate the force applied by the car. By multiplying the car's mass (1510 kg) with its acceleration, we will find the force.
Οnce we have the force, we can calculate the new acceleration if the 80 kg passenger rode along. Given that the force is constant, we determine the car's new acceleration by dividing this force with the new total mass (car mass + passenger's mass). So the question ultimately requires an application of the concepts of force, mass, and acceleration.
Learn more about Newton's second law and acceleration here:
The new acceleration of the Lamborghini Huracan with an added passenger can be calculated by finding the initial force using the car's mass and acceleration, and then using this force with the increased mass (original mass + passenger's mass) to find the new acceleration. The new acceleration will be less than the initial acceleration due to the increased mass.
To determine the new acceleration of the Lamborghini Huracan with an added passenger, we first calculate the initial force acting on the car. This can be done by using Newton's second law which states that Force = mass * acceleration. Initially, the acceleration is 0.80g (where g is acceleration due to gravity = 9.81 m/s²), and the mass is 1510 kg (including the driver). Therefore, the initial force = 1510 kg * 0.8 * 9.81 m/s².
However, when an 80-kg passenger rides along, the total mass becomes 1510 kg + 80 kg = 1590 kg. To find the new acceleration, we keep the force constant (as it is not affected by the introduction of the passenger) and rearrange the formula F = m*a as a = F/m. Use the increased mass to find the new acceleration. Please note that the new acceleration will be less than the initial acceleration due to increased mass.
A hemispherical surface (half of a spherical surface) of radius R is located in a uniform electric field of magnitude E that is parallel to the axis of the hemisphere. What is the magnitude of the electric flux through the hemisphere surface?
According to the definition of electric flux, it can be calculated integrating the product E*dA, across the surface.
As the electric field E is uniform and parallel to the hemisphere axis, and no charge is enclosed within it, the net flux will be zero, so, in magnitude, the flux across the opening defining the hemisphere, must be equal to the one across the surface.
The flux across the open surface can be expressed as follows:
As E is constant, and parallel to the surface vector dA at any point, can be taken out of the integral, which is just the area of the surface, π*R².
⇒Flux = E*π*R²
What is the correct formula for barium nitride? A. Ba3N2, в. BaN с. Ва2N3 D. Ba2N
The formula for barium nitride is Ba(NO3)2
As a science project, you drop a watermelon off the top of the Empire State Building. 320 m above the sidewalk. It so happens that Superman flies by at the instant you release the watermelon. Superman is headed straight down with a constant speed of 30 m/s. A) How much time passes before the watermelon has the same velocity? B) How fast is the watermelon going when it passes Superman?C) How fast is the watermelon traveling when it hits the ground?
3.06 seconds time passes before the watermelon has the same velocity
watermelon going at speed 59.9 m/s
watermelon traveling when it hits the ground at speed is 79.19 m/s
height = 320 m
speed = 30 m/s
to find out
How much time passes before the watermelon has the same velocity and How fast is the watermelon going and How fast is the watermelon traveling
we will use here equation of motion that is
v = u + at ....................1
here v is velocity 30 m/s and u is initial speed i.e zero and a is acceleration i.e 9.8 m/s²
put the value and find time t
30 = 0 + 9.8 (t)
t = 3.06 s
so 3.06 seconds time passes before the watermelon has the same velocity
we know superman cover distance is = velocity × time
so distance = 30 × t
and distance formula for watermelon is
distance = ut + 0.5×a×t² .............2
here u is initial speed i.e 0 and a is acceleration i.e 9.8 m/s² and h is 30 × t
30 × t = 0 + 0.5×9.8×t²
t = 6.12 s
so by equation 1
v = u + at
v = 0 + 9.8 ( 6.12)
v = 59.9 m/s
so watermelon going at speed 59.9 m/s
watermelon traveling speed formula is by equation of motion
v² - u² = 2as ......................3
here v is speed and u is initial speed i.e 0 and a is acceleration i.e 9.8 m/s² and s is distance i.e 320 m
v² - 0 = 2(9.8) 320
v = 79.19 m/s
so watermelon traveling when it hits the ground at speed is 79.19 m/s
Sharece knows that wave peaks and valleys can add and subtract. What would be the net effect if she was able to cross Wave 1 (a large-amplitude wave in a valley phase) with Wave 2 (a wave with slightly smaller amplitude than Wave 2, in a peak phase)?Sharece knows that wave peaks and valleys can add and subtract. What would be the net effect if she was able to cross Wave 1 (a large-amplitude wave in a valley phase) with Wave 2 (a wave with slightly smaller amplitude than Wave 2, in a peak phase)?
The two waves will add vectorially to produce a small amplitude wave in a valley phase.
The two waves will add vectorially to produce a small amplitude wave in a valley phase. This is because the amplitudes of the waves are slightly different and in opposite directions. When wave 1 cancels out all of wave 2, the resultant wave would be the slight difference between both waves, and it would be in the direction of wave 1 which is a valley phase.
A conveyor belt is used to move sand from one place to another in a factory. The conveyor is tilted at an angle of 18° above the horizontal and the sand is moved without slipping at the rate of 2 m/s. The sand is collected in a big drum 5 m below the end of the conveyor belt. Determine the horizontal distance between the end of the conveyor belt and the middle of the collecting drum.
The motion of sand is due to the movement of conveyor belt. The horizontal distance between the end of the conveyor belt and the middle of the collecting drum is 2.044 meters.
What is equation of motion?
The equation of motion is the relation between the distance, velocity, acceleration and time of a moving body.
The second equation of the motion for distance can be given as,
Here, is the initial body, is the acceleration of the body due to gravity and is the time taken by it.
The conveyor is tilted at an angle of 18° above the horizontal.
The Sand is moved without slipping at the rate of 2 m/s.
The sand is collected in a big drum 5 m below the end of the conveyor belt.
The horizontal component of the velocity is given as,
The vertical component of the velocity is given as,
Put the value in the above equation as,
The horizontal distance between the end of the conveyor belt and the middle of the collecting drum is,
Thus, the horizontal distance between the end of the conveyor belt and the middle of the collecting drum is 2.044 meters.