Question

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. The height (in feet) of a rocket launched from the ground is given by the function f(t) = -16t2 + 160t. Match each value of time elapsed (in seconds) after the rocket’s launch to the rocket's corresponding instantaneous velocity (in feet/second).

Answer 1

The pairs are;

t, v

2, 96

4, 32

5, 0

6, -32

7, -64

9, -128

Explanation:

The given equation is f(t) = -16·t² + 160·t

We have, the velocity, v = d(f(t))/dt = d(-16·t² + 160·t)/dt = -32·t + 160

Which gives;

t, v

0, -32×(0) + 160 = 160

1, -32×(1) + 160 = 128

2, -32×(2) + 160 = 96

3, -32×(3) + 160 = 64

4, -32×(4) + 160 = 32

5, -32×(5) + 160 = 0

6, -32×(6) + 160 = -32

7, -32×(7) + 160 = -64

8, -32×(8) + 160 = -96

9, -32×(9) + 160 = -128

The given velocity values are;

96, -64, 32, 0, -128, -32 which correspond to 2, 7, 4, 5, 9, 6

The pairs are;

t, v

2, 96

4, 32

5, 0

6, -32

7, -64

9, -128