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Liono4ka [1.6K]
2 years ago
7

When an object is thrown upwards with a speed of 64 ft/sec, its height above the ground is given by the function h(t)=−16t2+64t

, where t is the time in seconds after it has been thrown. At what time will the object reach its highest point?
Mathematics
1 answer:
Svet_ta [14]2 years ago
3 0

Answer:

The object will reach its highest point 0.5 seconds after it has been thrown.

Step-by-step explanation:

The object reaches its maximum height when velocity is equal to zero, the velocity is the derivative of function height. That is:

v(t) = \frac{d}{dt}h(t) (1)

Where v(t) is the velocity of the object at time t, in feet per seconds.

If we know that h(t) =-16\cdot t^{2}+64\cdot t and v(t) = 0\,\frac{ft}{s}, then the time when object reaches its highest point is:

v(t) = -32\cdot t+64

-32\cdot t + 64 = 0

t = 0.5\,s

The object will reach its highest point 0.5 seconds after it has been thrown.

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see the attached figure to better understand the problem

we know that

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