Question

A ball is dropped from a platform 19.6m high. Its position function is ______.

Options

• x = −4.9t² + 19.6 (0 ≤ t ≤ 1)

• x = −4.9t² + 19.6 (0 ≤ t ≤ 2)

• x = −9.8t² +19.6 (0  ≤ t ≤ 2)

• x = −4.9t² − 19.6 (0 ≤ t ≤ 2)

Answer 1

A ball is dropped from a platform 19.6m high. Its position function is x = −4.9t² + 19.6 (0 ≤ t ≤ 2).

Explanation:

We have, a = `(d^2x)/dt^2 = −9.8`

The initial conditions are x (0) = 19.6 and v (0) = 0

So, v = `dx/dt` = −9.8t + v(0) = −9.8t

∴ x = −4.9t² + x(0) = −4.9t² + 19.6

Now, the domain of the function is restricted since the ball hits the ground after a certain time. To find this time we set x = 0 and solve for t; 0 = − 4.9t² +19.6 ⇒ t = 2