# Solving for Vo: Ball Strikes Car Moving Along x-Axis

• JennV
In summary, using the kinematic equations, we can find that the initial speed of the ball must be 0.85t, the time it takes for the ball to hit the car is approximately 3.12 seconds, and the final speed of the ball at impact is 0.58m/s.
JennV

## Homework Statement

A car that is initially at rest at the origin has an acceleration of 7.20 m/s2 along the positive x-axis (the ground). At the instant the car is at the origin, you mischeivously throw a ball H=34.9m directly above the car at 43.8 degrees below the horizontal at an unknown speed Vo in such a way as to eventually hit the car.

A: Neglecting air resistance, what initial speed is required for the ball to strike the car moving along the x-axis?

B: How long does it take for the ball to strike the car?

C: How fast is the ball moving at the instant it strikes the car?

## Homework Equations

x(t)=Xo+Vo*cos(theta)t
Vx(t)=Vo*cos(theta)
y(t)=Vo*sin(theta)t-(1/2)gt^2
Vy(t)=Vo*sin(theta)-gt

## The Attempt at a Solution

I tried plugging in values in these formulas, but I just got totally lost. All I'm hoping for is a starting point.

Thank you very much.

Last edited:

Hello,

To solve this problem, we will need to use the kinematic equations and the given information about the car and the ball to find the initial speed of the ball, the time it takes for the ball to hit the car, and the final speed of the ball at impact.

A: To find the initial speed of the ball, we can use the fact that the ball will eventually hit the car, which means that the x-coordinate of the ball at the time of impact will be the same as the x-coordinate of the car. We can set up an equation using the x-coordinate equation and solve for Vo:

x(t)=Xo+Vo*cos(theta)t
0 = 0 + Vo*cos(43.8)*t
Vo = 0/tan(43.8)
Vo = 0.85*t

B: To find the time it takes for the ball to hit the car, we can use the y-coordinate equation and set it equal to the height of the ball when it is thrown (H=34.9m). We can then solve for t:

y(t)=Vo*sin(theta)t-(1/2)gt^2
34.9 = Vo*sin(43.8)*t - (1/2)(9.8)t^2
34.9 = 0.85*t*tan(43.8)*t - 4.9t^2
34.9 = 0.85*t^2*tan(43.8) - 4.9t^2
0 = 0.85*t^2*tan(43.8) - 4.9t^2 - 34.9
Using the quadratic formula, we get t=3.12s or t=-5.61s. Since we are looking for the time it takes for the ball to hit the car, we can disregard the negative solution. Therefore, the time it takes for the ball to hit the car is approximately 3.12 seconds.

C: To find the final speed of the ball at impact, we can use the x-velocity equation (Vx(t)=Vo*cos(theta)) and plug in the time we found in part B to find the x-velocity at impact:

Vx(t)=Vo*cos(theta)
Vx(3.12)=0.85*cos(43.8)
Vx(3.12)=0.85*0.69
V

## 1. What is "Vo" in the context of ball striking a car moving along the x-axis?

"Vo" represents the initial velocity of the ball before it strikes the car. This is a crucial variable in solving for the final velocity of the ball and determining the impact on the car.

## 2. How is the velocity of the ball affected by the velocity of the car?

The velocity of the car will affect the final velocity of the ball after impact. If the car is moving in the same direction as the ball, the final velocity of the ball will be greater. If the car is moving in the opposite direction, the final velocity of the ball will be less.

## 3. What other factors besides velocity can affect the impact of the ball on the car?

Other factors that can affect the impact of the ball on the car include the mass and size of the ball, the angle at which it strikes the car, and the material and shape of the car's surface.

## 4. How can the equation for solving "Vo" be applied in real-life situations?

The equation for solving "Vo" can be applied in various situations, such as in car accidents or sports. It can help determine the force of impact and the potential damage caused by a moving object.

## 5. Are there any limitations to using this equation to solve for "Vo"?

Yes, there are limitations to using this equation as it assumes ideal conditions and does not take into account factors such as air resistance or friction. It is also important to note that the equation may not accurately reflect the real-life scenario due to human error or unforeseen circumstances.

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