# What Is the Initial Velocity Required for a Cannonball to Hit a Moving Target?

• un_cooled
In summary: Xi - Xf + Vi(t) + (1/2)(gt^2) = Yi - Yf + Vi(t) + (1/2)(gt^2)Vi(4.49 s) - 198.78 m = 860.365 mVi(4.49 s) = 860.365 + 198.78 mVi = 1059.145 m/4.49 sVi = 235.89 m/s
un_cooled

## Homework Statement

A cannon which is at the top of a 99 m high cliff fires in a horizontal direction to a dog. The initial position of the dog is 1000 m from the cliff's base. What should be the initial velocity of the cannon if the dog is moving at constant speed of 9 m/s to the cliff.

Other given
square root of (198 m/9.8 m/s) = 4.49 s

## Homework Equations

Yf = Yi + Vi(t) + (1/2)(gt^2)
Xf = Xi + Vi(t) + (1/2)(gt^2)

## The Attempt at a Solution

For the y-component:

99 m = 0 + Vi(4.49 s) + (1/2)(-9.8 m/s^2)(4.49)^2
= Vi(4.49 s) -99.78 m - 99 m
= Vi(4.49 s) - 198.78 m

For the x-component:

0 m = 1000 m + (-9 m/s)(4.49 s) + (1/2)(-9.8 m/s^2)(4.5)^2
= 860.365 m

Then,

Xi - Xf + Vi(t) + (1/2)(gt^2) = Yi - Yf + Vi(t) + (1/2)(gt^2)
Vi(4.49 s) - 198.78 m = 860.365 m
Vi(4.49 s) = 860.365 + 198.78 m
Vi = 1059.145 m/4.49 s
Vi = 235.89 m/s

Can someone verify this? Thanks alot.

Could you explain what your notations mean? ehild

Yf = Yi + Vi(t) + (1/2)(gt^2)
Xf = Xi + Vi(t) + (1/2)(gt^2)

Yf = final position (y-axis)
Xf = final position (x-axis)
Vi = initial velocity
t = time
g = gravitational pull

Final and initial position of what? There are two moving things: the cannon ball and the dog. They start from different initial positions and they meet, so the final positions are the same for both of them. The ball accelerates downward, but the dog moves with constant velocity.

ehild

actually, I'm not sure about the equations that I used.

There are the Yi and Yf and Xi and Xf data for the ball, and xi and xf for the dog. As it moves on the ground, yi=yf=0. The position of both the ball and the dog are the same when the ball hits the dog, so Yf =0 and Xf=xf. You calculated the time needed to the ball to reach the ground, t=4.49 s. During that time the dog walked some distance, with constant velocity v= 9m/s towrds the cliff. So how far is it from the cliff when the ball hits the ground? The ball has to reach there at the same time as the dog.

You have to know that the motion of a projectile can be treated as two separate motions, one vertical with the downward acceleration -g, the other horizontal with constant velocity Vi. Instead of your equation, Xf=Xi +Vi t. But we measure the distance from the rock, so Xi=0, and Xf is the same as the distance of the dog from the cliff at time 4.49 s. Find Vi.

ehild

## 1. What is Kinematics problem solving?

Kinematics problem solving is a branch of physics that studies the motion of objects without considering the forces that cause the motion. It involves using equations and principles to analyze and solve problems related to the position, velocity, and acceleration of objects.

## 2. What are the key concepts in Kinematics problem solving?

The key concepts in Kinematics problem solving include displacement, velocity, acceleration, time, and the equations of motion (such as the equations of uniform motion and uniformly accelerated motion).

## 3. How do you approach solving a Kinematics problem?

The first step in solving a Kinematics problem is to identify the known and unknown quantities, and then choose the appropriate equation to use based on the given information. Next, substitute the known values into the equation and solve for the unknown quantity. Finally, double check your answer and make sure it is reasonable.

## 4. What are some common mistakes made when solving Kinematics problems?

Some common mistakes made when solving Kinematics problems include incorrect unit conversions, using the wrong equation, and forgetting to include negative signs for direction. It is important to carefully read the problem and pay attention to units and signs.

## 5. How can Kinematics problem solving be applied in real life?

Kinematics problem solving can be applied in real life situations such as calculating the speed and direction of a moving object, determining the distance traveled by a car in a certain amount of time, and predicting the motion of projectiles. It is also used in engineering and sports to optimize performance and design.

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