# Finding initial projectile velocity with angle and a point in the path?

• ICanHasHelp
In summary, the problem is asking to find the initial velocity of a ball hit at a 36 degree angle from the ground, which hits a target 30m ahead and 4m above the ground. Using the equations Vavg = Δd/Δt and aavg = Δv/Δt, and the given values, we can find the x and y components of the initial velocity. However, in order to isolate the unknown variable time, we need another equation. This can be found by using the y component of the motion. The correct equations for x and y components are Δx = (Vo * cos 36)Δt + 1/2ax(Δt)2 and Δy
ICanHasHelp

## Homework Statement

A ball is hit from the ground with an angle of 36 degrees above the horizontal. The ball hits a target 30m ahead and 4m above the ground. Find the initial velocity of the ball.

## Homework Equations

Vavg = Δd/Δt
aavg = Δv/Δt
Δd = voΔt + 1/2aΔt2

## The Attempt at a Solution

Δx = 30m
Δy = 4m
Vox = Vo * cos 36
Voy = Vo * sin 36
Δx = voxΔt + 1/2ax(Δt)2
Δx = (Vo * sin 36)Δt + 1/2ax(Δt)2
Since ax = 0 then
Δx = (Vo * sin 36)Δt

This question appeared on a quiz today and caught me totally by suprise. My teacher had never assigned homework questions like this ever and my textbook did not have any questions like it either. I've asked my teacher for help, but he didn't give me a clear answer. I've tried this question again at home for another two hours but I still couldn't get anything out of it. I know I have to find Δt, but I can't seem to isolate it. I would put all my attempts on the post, but I have already destroyed them in my fustration. Please help me! I'm losing my mind!

That is the correct equation for the x component of motion.

However, the reason your getting stuck is because you need another equation so that you can eliminate the unknown variable time.

This is where the y component of the motion will come in. Do this like you did to find the x component.

Remember: When the question asks for the initial velocity, it wants the velocity in the direction of launch, not a component of the velocity.

I'm sorry I didn't initially post it, but I did find Δy, which was

Δy = VoyΔt - -4.9m/s^2

I also tried substituting Δx/Δt in place of Vox and Δy/Δt for Voy, but I still could solve for Δt because Δt was always dividing the direction.

So first of all, the equation is delta Y = (Vo_y)*t + (1/2)(-9.8)t^2.

It should not be a minus negative 4.9. You also left off the t^2.

Also, your equation for delta x should be cos(36) not sin(36).

I understand your frustration with this question. It can be challenging to encounter a problem that you are not familiar with or have not been taught how to solve. However, as a scientist, it is important to approach problems with a logical and systematic approach. Let's break down the problem and see if we can find a solution.

First, we know that the ball is hit at an angle of 36 degrees above the horizontal. This means that the initial velocity of the ball can be represented as V0 = V0x + V0y, where V0x is the horizontal component and V0y is the vertical component. We can use trigonometric functions to determine these components. V0x = V0 * cos 36 and V0y = V0 * sin 36.

Next, we are given the distance and height of the target, which we can use to set up equations using the kinematic equations you have listed. However, we need to be careful in choosing which equations to use. Since we are looking for the initial velocity, we need to use equations that do not have time (Δt) as a variable. Let's use the equation Δy = V0yΔt + 1/2gt^2, where g is the acceleration due to gravity (9.8m/s^2). Plugging in our values, we get 4m = V0 * sin 36 * Δt + 1/2 * 9.8m/s^2 * Δt^2.

We also know that the ball travels a horizontal distance of 30m, so we can use the equation Δx = V0xΔt, which simplifies to 30m = V0 * cos 36 * Δt.

Now we have two equations with two unknowns (V0 and Δt). We can solve for Δt in the second equation and substitute it into the first equation to solve for V0. This will give us the initial velocity of the ball.

I hope this helps guide you towards finding a solution to this problem. Remember to approach problems systematically and use the appropriate equations. If you are still having trouble, don't hesitate to seek help from your teacher or a tutor. Keep up the good work in your studies!

## What is the formula for finding initial projectile velocity with angle and a point in the path?

The formula for finding initial projectile velocity with angle and a point in the path is V0 = (x - x0)/[(cosθ)(t - t0)], where V0 is the initial velocity, x is the final position, x0 is the initial position, θ is the angle of elevation, t is the final time, and t0 is the initial time.

## Can this formula be used for any type of projectile motion?

Yes, this formula can be used for any type of projectile motion as long as the initial and final positions, angle of elevation, and initial and final times are known.

## How accurate is this formula in finding the initial projectile velocity?

The formula is quite accurate, but may have slight errors due to factors such as air resistance and other external forces that may affect the projectile's motion.

## What units should be used for the variables in this formula?

The units for the variables in this formula should be consistent, such as using meters for position and seconds for time. The initial velocity will be in meters per second (m/s).

## Can this formula be used to find the initial velocity for a projectile that follows a curved path?

Yes, this formula can be used for a projectile that follows a curved path. However, it is important to note that the angle of elevation may change at different points in the path, so the initial velocity calculated may only be accurate for a specific point in the path.

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