Question

During a fireworks show, a rocket is fired vertically upward with an initial velocity of 200 meters per second. The height in meters, s, of the rocket in seconds, t, may be approximated by s = 200t – 5t2. The rocket must be at least 1,500 meters in the air to safely explode. In which time interval may it safely be exploded?

A.0 ≤ t ≤ 10 seconds
B.10 ≤ t ≤ 30 seconds
C.10 ≤ t ≤ 40 seconds
D.30 ≤ t ≤ 40 seconds

Answer 1

The rocket can safely explode in 10 ≤ t ≤ 30 seconds (see the last line of explanation).

Explanation:

The height of the rocket is shown by , where t is the time in seconds.

. The height will be maximum when, that is .

At t = 20, s = 4000 - 2000 = 2000.

The rocket can go 2000 meter maximum.

In order to explode safely, the rocket must be in a height equal or above 1500 meter.

When s = 1500,

Hence, at , the height .

Explanation:

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