A ball is shot from a compressed-air gun at twice its terminalspeed. (For the following, assume the drag force depends on v^{2})

1. What is the magnitude of the ball’s initial acceleration, as amultiple of * , if it is shotstraight up?Express your answer using one significantfigure. =*

2. What is the magnitude of the ball’s initial acceleration, as amultiple of * , if it is shotstraight down? Express your answer using one significantfigure. =*

**Acceleration**is the speed at which you the change speed of an object. It’s an abbreviation to describe increasing speed. It is an area of science known as Physics.

Scientists studying physics use a particular formula to calculate acceleration. The formula used to calculate acceleration is:

Acceleration = change in speed or time

The drag force magnitude is determined by Fd = -1/2*rho*v2*Cd*A.

Where rho represents the air density, v the velocity, and Cd the drag coefficient.

A is the cross-sectional area. The terminal velocity, vt will be equal to the gravitational force.

1/2*rho*vt^2*Cd*A = m*g

Because the drag force is proportional with the square of velocity, doubling the velocity will increase the drag force by a factor of 4.

Fd = 1/2*rho*(2*vt)^2*Cd*A

Fd = 1/2*rho*4*vt2*Cd*A

Fd = 4*(1/2*rho*vt^2*Cd*A)

Fd = 4*m*g

The drag force is therefore 4 times greater than the acceleration caused by gravity. m*a = 4*m*g

a = 4*g

The acceleration is 4*g. The drag force will always oppose the motion of the ball. If the ball is shot straight up gravity will oppose the drag force. This is how it works.

a = 4*g + 5g

a = 5*g

The drag force acts in the opposite direction of gravity when the ball is shot downwards.

a = 4*g – g

a = 3*g

Number 1 = 5, and number 2 = 3.