Question

The tallest roller coaster in the world used to be the Desperado in Nevada. It has a lift height of 64 m. If an archer shoots an arrow straight up in the air and the arrow passes the top of the roller coaster 3.0 s after the arrow is shot, what is the initial speed of the arrow?

Answer 1

Answer:

36 m/s

Explanation:

Time (t) = 3s

Displacement (s) = 64m

Acceleration (g) = -9.8m/s^2

Initial speed (u) = ?

Use the following equation:

s = ut + 1/2 at^2

64 = u*3 + 0.5 * -9.8 * 3^2

64 = 3u - 44.1

u = 36.03m/s

Answer 2

The initial speed of the arrow is 36.03 m/s

The given parameter:

the lift height, h = 64 m

time taken to reach the top of the roller coaster, t = 3.0 s

To find:

• the initial speed of the arrow

The initial speed of the arrow is calculated by using the following kinematic equation:

$h = ut - \frac{1}{2} gt^2\\\\where;\\\\u \ is \ the \ initial\ speed\\\\64 = 3t- (0.5\times 9.8 \times 3^2)\\\\64 = 3t - 44.1\\\\3t = 64 + 44.1\\\\t = \frac{108.1}{3} \\\\t = 36.03 \ m/s$

Thus, the initial speed of the arrow is 36.03 m/s

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