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.

Solutions

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 1 year ago

Next > < Previous

Related Solutions

An arrow is shot straight up from a horizontal level with an initial velocity of 45j...

An arrow is shot straight up from a horizontal level with an initial velocity of 45j m/s. A. Find its flight time. B. Find its position at t=6.0s C. What is its velocity at t=6.0s D. Graph v(t) vs. t.

From the castle wall 20m high shot an arrow. The initial speed of the bow is...

From the castle wall 20m high shot an arrow. The initial speed of the bow is 45 m/s directed 40 degrees above the horizontal. Find the initial velocity components. Find the maximum height of the arrow. Find the range. Find an arrow final velocity.

If an arrow is shot upward on Mars with a speed of 68 m/s, its height...

If an arrow is shot upward on Mars with a speed of 68 m/s, its height in meters t seconds later is given by y = 68t − 1.86t2. (Round your answers to two decimal places.) (a) Find the average speed over the given time intervals. Estimate the speed when t = 1.

A ball is thrown straight up with an initial speed of 19 m/s. The ball was...

A ball is thrown straight up with an initial speed of 19 m/s. The ball was released 6.3 m above the ground, but when it returns back down, it falls into a hole d m deep. If the ball’s speed is 35.7 m/s at the bottom of the hole, how deep is the hole (in m)?

During a fireworks display, a shell is shot into the air with an initial speed of...

During a fireworks display, a shell is shot into the air with an initial speed of 91.55 m/s at an angle of theta degrees above the horizontal. The fuse is timed to 8.21 seconds for the shell just as it reaches its highest point above the ground. If the horizontal displacement of the shell is 149.68 meters when it explodes, what is the height (in unit of meters) when the shell explodes? You must use g = 9.8 m/s2.

A projectile is shot straight up from the earth's surface at a speed of 5000km/hr ....

A projectile is shot straight up from the earth's surface at a speed of 5000km/hr . How high does it go? Express your answer with the appropriate units.

A ball of mass m is shot straight up into the air by a spring-loaded launcher....

A ball of mass m is shot straight up into the air by a spring-loaded launcher. Initially, the spring is compressed by a distance D. After the spring is released, the ball has a velocity v out of the launcher and finally reaches a maximum height H. Ignoring air resistance, which of the following statements are true? True False If the spring constant is doubled, the ball will max out at height 8H True False The initial potential energy of the spring...

You shoot an arrow into the air at an initial velocity of 12.5m/s at an angle...

You shoot an arrow into the air at an initial velocity of 12.5m/s at an angle of 40º. Find the maximum height the arrow reaches in the air. Find the time it takes to reach its maximum height. Find the time it takes to hit the ground. Assume its flight in the air is symmetrical, with the first half of flight traveling upward, and the 2nd half of flight traveling downward. Find how far away it hits the ground.

a ball thrown straight up returns to its starting height in 7.2s.its initial speed was----------m/s.

1. A man walks along a straight path at a speed of π ft/s. A searchlight...

1. A man walks along a straight path at a speed of π ft/s. A searchlight is located on the ground 18 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 30 ft from the searchlight? Draw a picture first to understand the problem. 2. Suppose square ABCD has straight edges of length 2, and its corners are connected by hinges. When pulling corners A and C,...

Subjects