Question

The height of an object thrown upward with an initial velocity of 32 feet per second is given by the formula h = −16t2 + 32t, where t is the time in seconds. How long will it take the object to reach a height of 16 feet?

Answer 1

Answer:

Therefore  after 1 second of lunched the object reach a height of 16 feet.

Step-by-step explanation:

When a particle is thrown vertically upward direction on that time only gravitation force is worked on it. In that case the acceleration of the particle is - g.Since gravitation force works downward direction and the displacement of the particle is upward direction that's why acceleration is negative.

When particle comes down the the acceleration of the particle is g.

Since the displacement and acceleration work on the particle in same direction.

The value of g is 9.8 m/s².

Given that, the height of the particle can measure from the equation

$h=-16t^2+32t$       Where t is time in second

To find out the time when the object reach a height 16 feet. We have put the value of h in the given equation.

Putting h=16 in the given equation

16= -16 t²+32

⇒16t²-32t+16=0

⇒16(t²-2t+1)=0

⇒t²-2t+1=0²         [ ∵16≠0]

⇒(t-1)²=0

⇒t-1=0

⇒t=1

Therefore  after 1 second of lunched the object reach a height of 16 feet.