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.