Question

A dog jumps straight up in the air to catch a ball and lands on the ground 1.3 s later. Let h(t) represent the dog’s height, in meters, t seconds after he leaves the ground. Which equation models the dog’s height for a given time t?

A. h(t) = –9.8t2 + 12.74t
B. h(t) = –4.9t2 + 6.37t
C. h(t) = –9.8t + 12.74t
D. h(t) = –4.9t + 6.37t

Answer 1

The given question have mistake. The correct question is written below.

Question:

A dog jumps straight up in the air to catch a ball and lands on the ground 6.37 s later. Let h(t) represent the dog’s height, in meters, t seconds after he leaves the ground. Which equation models the dog’s height for a given time t?

Answer:

Option B:

`h(t)=-4.9 t^(2)+6.37t`

Solution:

General formula for the height of the projectile over time:

(1)
`h(t)=-16 t^(2)+v t+s`

Where h = height in feet, t = time, v = initial velocity and s = initial height (feet)

(2)
`h(t)=-4.9 t^(2)+v t+s`

Where h = height in meters, t = time, v = initial velocity and s = initial height(meter)

Given initial velocity = 6.37 s and initial height is 0.

The height of the dog is in meters.

So, use second formula and substitute v = 6.37 and s = 0.

`h(t)=-4.9 t^(2)+v t+s`

`h(t)=-4.9 t^(2)+6.37t+0`

`h(t)=-4.9 t^(2)+6.37t`

Hence option B is the correct answer.