Question

A quarterback throws a football to a teammate. The football is 6.5ft above the ground when it leaves the quarterback's hand. His teammate catches it 3.5s later, at a height above the ground of 5 ft. Projectile motion formula h(t) = -16t2 + vt + h0 h0 = 6.5 v = ? h = 5 when t = 3.5 Determine the value of v, rounded to the nearest whole number.

Answer 1

The value of v, rounded to the nearest whole number = 56 ft/s

Explanation:

The equation of Projectile motion formula is

h(t) = -16t² + vt + h₀

We have h₀ = 6.5

Substituting

h(t) = -16t² + vt + 6.5

h = 5 when t = 3.5, that is h(3.5) = 5

Substituting

h(3.5) = -16 x 3.5² + v x 3.5 + 6.5 = 5

3.5v = 194.5

v = 55.57 ft/s = 56 ft/s

The value of v, rounded to the nearest whole number = 56 ft/s

Answer 2

Answer: v= 56 ft per second

Explanation:

Given: A quarterback throws a football to a teammate.

Projectile motion formula is given by :-

`h(t)=-16t^2+vt+h_0`, where
`h_0=6.5`

Now, to find v at h=5 and t=3.5, substitute these values in the above equations, we get

`5=-16(3.5)^2+v(3.5)+6.5\\\Rightarrow5=-16(12.25)+3.5v+6.5\\\Rightarrow5=-196+6.5+3.5v\\\Rightarrow\ 5=-189.5+3.5v\\\Rightarrow\ 3.5v=5+189.5\\\Rightarrow\ 3.5v=194.5\\\Rightarrow\ v=55.57142\approx56`