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Natali5045456 [20]
4 years ago
12

A pomegranate is thrown from ground level straight up into the air at time t=0 with velocity 240 feet per second. Its height in

feet at t seconds is f(t)=-16 t^2+240 t. Find the time it hits the ground and the time it reaches its highest point. Hits the ground when t= 4 second (include units) Reaches highest point when t= 2 second (include units) Maximum height =
Physics
1 answer:
3241004551 [841]4 years ago
6 0

Answer:

a) t=15 s

b) t=7.5s

c) f(t)=900ft

Explanation:

From the exercise we have the equation of height and the initial velocity of the pomegranate

f(t)=240t-16t^{2}

a)To find the time that it hits the ground we know that its position is 0

0=240t-16t^{2}

Solving for t using quadratic equation

t=\frac{-b±\sqrt{b^{2}-4ac } }{2a}

a=-16\\b=240\\c=0

t=0s or t=15s

Since time can not be 0, the answer is t=15s

b) To find the time that it reaches its highest point we need to analyze the velocity at that time

v=\frac{df}{dt}

\frac{dt}{dt}=240-32t

At the highest point its velocity is 0

0=240-32t

t=\frac{240ft/s}{32ft/s^{2} }=7.5s

c) To find the maximum height we need to use f(t) with t=7.5

f(t)=240(7.5)-16(7.5)^{2}=900ft

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