Question

A penny is kicked horizontally off the roof of a 10-story building (33.3 m high) and lands 52 m away on the ground. A) what is the pennys initial vertical velocity?
B) HOw long is the penny in the air?
C) what is the penny's initial horizontal velocity?
D) What is the pennys speed when it hits the ground?

Answer 1

A) The penny was kicked horizontally off the building. By this very statement, the penny had 0 initial vertical velocity.

B) Apply the following kinematics equation to the penny's vertical motion:

D = Vt + 0.5At²

D = vertical distance traveled, t = time, V = initial vertical velocity, A = vertical acceleration

Given values:

D = 33.3m, V = 0m/s, A = 9.81m/s²

Plug in and solve for t:

33.3 = 4.905t²

t = 2.61s

C) The penny fell for 2.61 seconds, therefore it moved horizontally for 2.61 seconds.

v = x/t

v = horizontal velocity, x = horizontal distance traveled, t = time

Given values:

x = 52m, t = 2.61s

Plug in and solve for v:

v = 52/2.61

v = 19.9m/s

D) Let's calculate the penny's vertical speed right before it hits the ground:

v = at

v = final vertical speed, a = vertical acceleration, t = time

Given values:

a = 9.81m/s², t = 2.61s

Plug in and solve for v:

v = 9.81(2.61)

v = 25.6m/s

Use the Pythagorean theorem to find the final speed:

V = √(Vx²+Vy²)

V = final speed, Vx = final horizontal speed, Vy = final vertical speed

Given values:

Vx = 19.9m/s, Vy = 25.6m/s

Plug in and solve for V:

V = √(19.9²+25.6²)

V = 32.4m/s