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
