1)A rock is projected from the edge of the top of a building with an initial vel

Question

1)A rock is projected from the edge of the top of
a building with an initial velocity of 18.6 m/s
at an angle of 32?
above the horizontal. The
rock strikes the ground a horizontal distance
of 98 m from the base of the building.
The acceleration of gravity is 9.8 m/s2.
Assume: The ground is level and that the
side of the building is vertical. Neglect air
friction.What is the horizontal component of the
rock’s velocity when it strikes the ground?
Answer in units of m/s


2)How long does the rock remain airborne?
Answer in units of s

3)How tall is the building? answer in units of m

4)What is the vertical component of the rock’s
velocity when it strikes the ground?
Answer in units of m/s


5)What is the magnitude of the rock’s velocity
when it strikes the ground?
Answer in units of m/s

Explanation / Answer

Not much time left so I'm going to do this fast. I hope that you know the formulas that I will use.

1.) Use a triangle to break down the inital velocity. The x=18.6cos(32) and y=18.6sin(32)

x=15.51 m/s and y = 10.256 m/s

2.) Now that we know the rock's velocity in the x direction, we know that it doesn't change with time beceause gravity is only in the y. So you can use Distance=Rate(in the x)*Time.

98=15.51t

t=6.31 seconds

3&4.) You know the initial velocity in the y. Using (Final velocity)^2 = (Initial velocity)^2 + 2*acceleration*distance. You can find the distance from the top of the duilding. You know at the top of the parabolic projection patht the final velocity is 0. So you get 0 = 10.256^2 +2*-9.81*d. d = 5.361 m above the inital top of the building.

Now using the time we found earlier, we know Final velocity = initial velocity + a*t. Knowing at the top of the path, the initail velocity is 0, Vfy = 0 + 6.31*-9.81 Vfy= -61.9 m/s

Using (Final velocity)^2 = (Initial velocity)^2 + 2*acceleration*distance again we can find the distance it was in the air. 61.9^2 = 0 + 2*9.81*d d = 195.29m

5.) Using Pythagorian's theroem you know that Vfx^2 + Vfy^2 = Vf^2 (15.51^2) + (-61.9^2) = Vf^2

Vf = 63.82 m/s

Hope that helps and wasn't to comfusing with out pictures.

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