Question

A quarterback throws a football toward a receiver from a height of 6 ft. The initial vertical velocity of the ball is 14 ft/s. At the same time that the ball is thrown, the receiver raises his hands to a height of 8 ft and jumps up with an initial vertical velocity of 10 ft/s. Projectile motion formula: h = -16t2 + vt + h0 t = time, in seconds, since the ball was thrown h = height, in feet, above the ground { complete the system that models the heights of the ball and the receiver's hands over time.

Answer 1

6,10,8

Explanation:

h = -16t2 + vt + h0

t = time, in seconds, since the ball was thrown

h = height, in feet, above the ground

h = -16t² + 14t +

h = -16t² +

t

+

Answer 2

Given the projectile formula:

`h = -16t^2+vt+h_0`

where, t is the time in second.

As per the statement:

A quarterback throws a football toward a receiver from a height of 6 ft. The initial vertical velocity of the ball is 14 ft/s

⇒
`h_0 = 6 ft` and v= 14 ft/s

Substitute these given values we have;

`h = -16t^2+14t+6`

It is also given that at the same time that the ball is thrown, the receiver raises his hands to a height of 8 ft and jumps up with an initial vertical velocity of 10 ft/s.

⇒
`h_0 = 8 ft` and v= 10 ft/s

then;

`h = -16t^2+10t+8`

Therefore, the system that models the heights of the ball and the receiver's hands over time :

`h = -16t^2+14t+6`

`h = -16t^2+10t+8`