Question

The Sunshine Skyway Bridge is 131 m high. A truck crossing the bridge loses a piece of cargo, launching it horizontally and perpendicularly off the bridge at 75 miles per hour. How far does the object travel horizontally before it hits the water?

102 m

118 m

137 m

155 m

173 m

The Sunshine Skyway Bridge is 131 m high. A truck crossing the bridge loses a piece of cargo, launching it horizontally and perpendicularly off the bridge at 75 miles per hour. How fast is it going when it hits the water?

79.3 m/s

33.5 m/s

50.7 m/s

57.4 m/s

60.7 m/s

Answer 1

1 mile = 1609.344 meter

1 hour = 3600 sec

Let us consider the downwards direction as positive.

Gravitational acceleration = g = 9.8 m/s²

Initial velocity of the cargo = V₁ = 75 mi/hr = 75 x (1609.344/3600) m/s = 33.528 m/s

The cargo is launched horizontally therefore,

Initial horizontal velocity of the cargo = V_1x = 33.528 m/s

Initial vertical velocity of the cargo = V_1y = 0 m/s

Height of the bridge = H = 131 m

Time taken by the cargo to reach the water = T

T = 5.17 sec

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

Horizontal distance covered by the cargo before hitting the water = R

R = 173 m

Velocity of the cargo when it hits the water = V₂

Horizontal velocity of the cargo when it hits the water = V_2x

V_2x = V_1x

V_2x = 33.528 m/s

Vertical velocity of the cargo when it hits the water = V_2y

V_2y = 50.666 m/s

V₂ = 60.7 m/s

a) Horizontal distance the cargo travels before hitting the water = 173 m

b) Speed of the cargo when it hits the water = 60.7 m/s