Question

In: Physics

An arrow is shot straight up in the air with an initial speed of 240 ft/s....

An arrow is shot straight up in the air with an initial speed of 240 ft/s. If on striking the ground it embeds itself 8.00 in into the ground, find the magnitude of the acceleration (assumed constant) required to stop the arrow, in units of feet/second^2.

Expert Solution

The arrow is fired at a speed of 240 ft/s straight up into the air.

The arrow reaches a maximum height, then falls. After striking the ground it deaccelerates and travels 8 in into the ground.

We are required to find this deacceleration which stops the arrow from penetrating further.

At the highest point velocity of the arrow is 0 ft/s.

Hence time required to reach the maximum height is

Maximum height reached by the arrow is

By the principle of conservation of energy

At the topmost position kinetic energy is zero as velocity is zero. At the bottom potential energy is 0 as h=0.

Where v is the velocity with which the arrow strikes the ground.

Now it decelerates and embeds itself to the ground.

Here v=0 as it finally comes to rest

This is the acceleration(rather deacceleration) required to stop the arrow.

genius_generous answered 2 years ago

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