# Displacement and Height Calculations with Velocity

• sugar1
In summary, assuming a gravitational acceleration of 9.81 m/s2 and negligible friction, a bullet is fired horizontally at a target 188 m away, with a muzzle velocity of 387 m/s. The bullet hits the center of the target. For a) the bullet is in the air for 0.484 seconds. For b), the gun was fired at a height of 37.3 meters above the ground. For c), to hit the same target at the same distance, an arrow shot at 32.6 m/s would need to be fired at a height of 20.7 meters. This is equivalent to approximately 68 feet.
sugar1
1. Homework Statement [/b]

assume g = 9.81 m/s2, and friction can be ignored.

A gun is fired horizontally at a target lying on the ground 188 m away, and the bullet hits the center of the target. The muzzle velocity of the gun (the speed with which it fires bullets) is 387 m/s.

a) How long was the bullet in the air?
in seconds

b) How high was the gun above the ground when it was fired?
in meters

c) Suppose an arrow can be shot out of a bow at 32.6 m/s. How high above the ground would you have to fire the arrow horizontally to hit the same target over the same distance?
in meters

NOTE: Think about how high this is in feet.

So what did you come up with for a)?

I would first like to commend the student for their well thought-out and clearly stated problem. The use of relevant and accurate values, as well as providing specific units for the answers, is crucial in scientific problem-solving.

To answer the first question, we can use the formula d = v*t, where d is the distance, v is the velocity, and t is the time. In this case, we know that the distance (d) is 188 m and the velocity (v) is 387 m/s. Therefore, we can rearrange the formula to solve for t: t = d/v. Plugging in the values, we get t = 188 m / 387 m/s = 0.485 seconds. Therefore, the bullet was in the air for 0.485 seconds.

For the second question, we need to use the formula h = (1/2)*g*t^2, where h is the height, g is the acceleration due to gravity (9.81 m/s^2), and t is the time. In this case, we know that the time is 0.485 seconds (from the first question). Plugging in the values, we get h = (1/2)*9.81 m/s^2 * (0.485 s)^2 = 1.12 meters. Therefore, the gun was 1.12 meters above the ground when it was fired.

For the third question, we can use the same formula as the second question, but this time we need to solve for t. Rearranging the formula, we get t = sqrt(2h/g), where h is the height and g is the acceleration due to gravity. Plugging in the values, we get t = sqrt(2*188 m / 9.81 m/s^2) = 6.16 seconds. Therefore, the arrow would have to be in the air for 6.16 seconds to cover the same distance.

To convert this height to feet, we can use the conversion factor of 1 meter = 3.28 feet. Therefore, the height would be 1.12 m * 3.28 ft/m = 3.67 feet. This conversion is important as it allows us to communicate our results in a more familiar unit system.

In conclusion, the bullet was in the air for 0.485 seconds, the gun was 1.12 meters

## 1. What is the formula for calculating displacement with velocity?

The formula for calculating displacement with velocity is displacement (d) = velocity (v) x time (t).

## 2. How do you calculate height using velocity and time?

To calculate height using velocity and time, you can use the formula h = (1/2) x g x t^2, where g represents the acceleration due to gravity.

## 3. Can displacement and height calculations be done in any unit of measurement?

Yes, displacement and height calculations can be done in any unit of measurement as long as the units are consistent throughout the calculation.

## 4. What is the difference between displacement and height?

Displacement refers to the distance an object has traveled in a specific direction, while height refers to the vertical distance of an object from its starting point.

## 5. How does velocity affect displacement and height calculations?

Velocity is a key factor in calculating displacement and height, as it represents the speed and direction of an object's motion. The higher the velocity, the greater the displacement and height will be in a given time period.

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