Question

A particle is moving along a projectile path where the initial height is 96 feet with an initial speed of 16 feet per second. What is the maximum height of the particle?

100 feet
96 feet
60 feet
56 feet

Answer 1

Answer: 100 feet. A

Explanation:

I took the test. Got it right

Answer 2

The maximum height of the particle is 100 ft

A is correct

Explanation:

A particle is moving along a projectile path where the initial height is 96 feet with an initial speed of 16 feet per second.

The standard equation of parabolic projectile.

`h(t)=-16t^2+v_0t+h_0`

where,

`v_0=16\ ft/s`

`h_0=96\ ft`

`h(t)=-16t^2+16t+96`

So, we get the parabolic equation of path.

The maximum value at vertex.

`t=-(b)/(2a)`

`t=-(16)/(-32)=(1)/(2)`

Maximum at t=0.5

`h(0.5)=-16(0.5)^2+16(0.5)+96`

`h(0.5)=100`

Hence, The maximum height of the particle is 100 ft