Question

Match each scenario involving projectile motion with the equation that describes the height of the object at time t. Tiles h = -4.9t2 + 5 h = -4.9t2 + 1.5 h = -16t2 + 73t + 1.5 h = -16t2 + 5 h = -16t2 + 73t + 5 h = -4.9t2 + 73t + 1.5 Pairs Dwayne throws a ball with an initial velocity of 73 feet/second. Dwayne holds the ball 5 feet off the ground before throwing it. A watermelon falls from a height of 5 feet to splatter on the ground below. Marcella shoots a foam dart at a target. She holds the dart gun 1.5 meters off the ground before firing. The dart leaves the gun traveling 73 meters/second. Greg drops a life raft off the side of a boat 1.5 meters above the water.

Answer 1

1. h = -16t^2 + 73t + 5
2. h = -16t^2 + 5
3. h = -4.9t^2 + 73t + 1.5
4. h = -4.9t^2 + 1.5

Explanation:

The general equation we use for ballistic motion is ...

`h(t)=(1)/(2)gt^2+v_0t+h_0`

where g is the acceleration due to gravity, v₀ is the initial upward velocity, and h₀ is the initial height.

The values of g commonly used are -32 ft/s², or -4.9 m/s². Units are consistent when the former is used with velocity in ft/s and height in feet. The latter is used when velocity is in m/s, and height is in meters.

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Dwayne throws a ball with an initial velocity of 73 feet/second. Dwayne holds the ball 5 feet off the ground before throwing it. (h = -16t^2 + 73t + 5)

A watermelon falls from a height of 5 feet to splatter on the ground below. (h = -16t^2 + 5)

Marcella shoots a foam dart at a target. She holds the dart gun 1.5 meters off the ground before firing. The dart leaves the gun traveling 73 meters/second. (h = -4.9t^2 + 73t + 1.5)

Greg drops a life raft off the side of a boat 1.5 meters above the water. (h = -4.9t^2 + 1.5)

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Additional comment on these scenarios

The dart and ball are described as being launched at 73 units per second. Generally, we expect launches of these kinds of objects to have a significant horizontal component. However, these equations are only for vertical motion, so we must assume the launches are straight up (or that the up-directed component of motion is 73 units/second).