Question

Tom, Spock, and McCoy stand on the top deck of a parking garage on planet Earth, 17 m above the ground below. For reasons that are unknown to us, they simultaneously throw pebbles off the deck, each at the same speed of 8 m/s. Tom throws his up at an angle of 45 degrees above the horizontal, Spock throws his perfectly horizontally, and McCoy, in a fit of pique, throws his straight down toward the ground. How far does Tom's stone land from the edge of the garage in meters?

Answer 1

Let us assume the upwards direction as positive and the downwards direction as negative.

Gravitational acceleration = g = -9.81 m/s²

Velocity at which Tom throws the stone = V = 8 m/s

Angle at which Tom throws the stone = = 45^o

Initial horizontal velocity of the stone = V_x = VCos = (8)Cos(45) = 5.66 m/s

Initial vertical velocity of the stone = V_y = VSin = (8)Sin(45) = 5.66 m/s

Height of the top deck of the parking garage = H = 17 m

Time taken for the stone to reach the ground = T

When the rock reaches the ground the vertical displacement of the stone is downwards therefore it is negative.

-H = V_yT + gT²/2

-17 = (5.66)T + (-9.81)T²/2

4.905T² - 5.66T - 17 = 0

T = 2.526 sec or -1.372 sec

Time cannot be negative.

T = 2.526 sec

Horizontal distance traveled by the stone = R

There is no horizontal force acting on the stone therefore the horizontal velocity of the stone remains constant.

R = V_xT

R = (5.66)(2.526)

R = 14.3 m

Distance of the point where Tom's stone lands from the edge of the garage = 14.3 m