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2. A stone is launched straight up by a slingshot. It has an initial speed of 28.0 m/s, and the stone is 1.60 m above the ground when launched.

(a) Determine the maximum height the stone reaches above the ground.
(b) Calculate the time it takes for the stone to hit the ground.
(c) Find the magnitude and direction of the stone's velocity just before it hits the ground.

User Zuzana
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1 Answer

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Final answer:

The stone reaches a maximum height of 40.82 meters. It takes approximately 5.71 seconds for the stone to hit the ground. The magnitude of the stone's velocity just before it hits the ground is 28.0 m/s, and the direction is downwards.

Step-by-step explanation:

(a) The maximum height a projectile reaches can be calculated using the equation:

max height = initial velocity squared / (2 * acceleration due to gravity)

Plugging in the given values, we get:

max height = (28.0 m/s)^2 / (2 * 9.8 m/s^2) = 40.82 m

So, the maximum height the stone reaches above the ground is 40.82 meters.

(b) The time it takes for the stone to hit the ground can be calculated using the equation:

time = 2 * (initial velocity / acceleration due to gravity)

Plugging in the given values, we get:

time = 2 * (28.0 m/s / 9.8 m/s^2) = 5.71 s

So, it takes approximately 5.71 seconds for the stone to hit the ground.

(c) When the stone hits the ground, its velocity will be the same magnitude as its initial velocity, but in the opposite direction. So, the magnitude of the stone's velocity just before it hits the ground is 28.0 m/s, and the direction is downwards.

User Fabio Nolasco
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