Pls help with homework! KINEMATICS: Uniform Acceleration, Free Fall , and Projectile

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Can you answer this for me pls? I need this tomorrow and I still have so much work in hand. This questions are about Kinematics. pls help me. with solutions pls :)

• The World Trade Center and the Empire State Building in the “Big Apple” have heights of 417 m and 381 m respectively. If objects were dropped from the top of each, assuming free fall,
(a) what would be the difference in time of their reaching the ground?
(b) What initial velocity should be imparted on the later object to reach the ground so that both objects will have the same times of fall and therefore strike the ground at the same time?

• Eunice throws a volleyball ball vertically upward with an initial speed of 9.8 m/s. Another student , Elaine, standing 5.0 m away, starts running toward the ball upon release and catches it at the same height of release. What was the horizontal acceleration of Elaine? (Assume uniform acceleration.)

• A kangaroo jumps to a vertical height of 2.7 m. How long was it in air before returning to the ground?

• The famous British spy, James Bond, is standing on a bridge 20.0 m above the railway and his enemies are getting too near for his capture. At that moment, 1/10 of a 100.0 m long high-velocity train is passing at 10.0 m/s under the bridge with an acceleration of 2.0 m/s2. For his escape, he jumped from the bridge towards the top of the train. Will his timing and the time of the passing train be a perfect escape factor to enable his landing on the last 1/10 m of the escape train? Prove your answer.

• Prince Juan found the Quetzalcotl asleep at the top of a tall kapok tree. The exhausted prince sits belowground to wait for the bird to wake up. Unfortunately, the sleeping bird release its dropping, which lands on Prince Juan’s unprotected head after 2.8 s.
(a) Assuming the dropping fell freely without impediments, what is the bird dropping’s speed just before hitting Prince Juan’s poor head?
(b) Find the location (dy) of the Quetzalcotl from the top of Prince Juan’s head.

• A student at a window on the second floor of a dormitory sees her archenemy coming along the walkway on the side of the building. She drops a water balloon 18.0 m above the ground when her enemy is 1.00 m from the point directly beneath the window. If the hated enemy is 1.70 m tall and walks at a rate of 0.450 m/s, does the balloon hit his head? Prove your answer.

• A photojournalist is on assignment documenting the search and rescue mission for the missing helicopter carrying a senator and team off the coast of some island. She accidentally drops her camera when the helicopter she was riding is 60.0 m above the ground.
(a) Assuming there is no air resistance, how long will it take the camera to reach the water?
(b) If the camera is shockproof to impact speeds of 200.0 m/s on water, will the camera be shattered?

• Juliet’s balcony is too high for Romeo to climb into. Desiring to catch the attention of a forlorn Romeo below, Juliet threw a pebble downward with an initial speed of 5.40 m/s from a height of 12.0 m above the ground.
(a) How far does the stone travel in 5.00 s?
(b) What is its velocity when it hits the ground?

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  • #2
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Before anybody can give help, you need to post your attempt. This can be what you understand so far, your calculations and any reasoning.
  • #3

The problems above concern vertical projectile motion. In order to do this effectively, you must remind yourself of the equations of motion for constant linear velocity.
vf = vi + aΔt
Δx = viΔt + 1/2 aΔt^2
vf^2 = vi^2 + 2aΔx
Δx = ([vi+vf]/2)Δt

(Where ^2 = squared, vf = final velocity, vi = initial velocity, Δt = change in time, Δx = change in displacement. )

I will help a bit with question one to jog your memory.
The objects are released from the thrower's hand directly downwards and are not thrown upwards beforehand thus each object on each building falls from rest so we have a initial velocity of 0 (vi = 0). In order to calculate the time difference between the two objects that fall from each building, we first need to know how long each object takes to reach the ground from each respective building.

As initial velocity (vi) is zero, we can simplify the above sets of equations to two cases:

vf = gΔt and x = 1/2gΔt^2

We would use the second equation above as we have x (the height of each building in this case), we know that if an object falls from rest, and there are no opposing forces such as air friction that the only force acting on the object is gravitational acceleration which is 9,8 m/s and thus we can work out time in the equation above.

So for question 1 a)
The time taken for the object to fall from the World Trade Center is:
(we have decided to choose our reference point to be Earth so gravitational acceleration is positive, you could do it the other way around and choose the point dropped to be your reference point in which case, gravitational acceleration is - but then the signs of positions and velocities have to change accordingly)
x = 1/2gΔt^2
therefore 417 = 1/2(9,8)Δt^2
so t = 9,23. You would then do the same for the second building and find the difference in time.

I hope this helps somewhat and that I have not made a mistake in my explanation as I am in a rush, give us what you have done so far and we will attempt to help but you must show that you have put some effort in atleast!
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