# How to find the muzzle velocity of a launcher?

I'm currently working a lab that requires me to find the muzzle velocity (initial velocity) of my launcher. The only information I have is the launch angle, horizontal distance, maximum height and time. Is there a specific equation that I have to use? Should I be using trig equations with projectile motion equations?

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I'm currently working a lab that requires me to find the muzzle velocity (initial velocity) of my launcher. The only information I have is the launch angle, horizontal distance, maximum height and time. Is there a specific equation that I have to use? Should I be using trig equations with projectile motion equations?
Yes

Alright but which ones?

Bandersnatch
Alright but which ones?
You need to choose a motion equation that contains initial velocity and doesn't contain any variables whose values are not specified in the problem.

Alternatively, use conservation of energy.

Okay say the launch angle is at 90 degrees, max.height is 110cm, horizontal range is 525cm, time is 2.4s, what equation would i use to solve for initial velocity?

Orodruin
Staff Emeritus
Homework Helper
Gold Member
Are you familiar with parabolic motion? If so you should be able to derive a relationship between some of the quantities that you have.

Okay say the launch angle is at 90 degrees, max.height is 110cm, horizontal range is 525cm, time is 2.4s, what equation would i use to solve for initial velocity?
These values are inconsistent. If you fire straight up into the air, how is the projectile going to get a horizontal velocity component?

Opps I meant 45 degree sorry about that but thank you

Bandersnatch
What kinematic equations do you know? Which one do YOU think you should use?
Perhaps you know how to write down a conservation of energy equation instead?

This is a homework-type question, and we are not supposed to give you a straight answer. You need to show some work.

mfb
Mentor
Opps I meant 45 degree sorry about that but thank you
Still inconsistent.
Actually, if you have so many known quantities, you have multiple independent ways to calculate those values and you can check if they agree with each other.

Even after setting the launch angle at 45 degrees, the values are still inconsistent. If the projectile is in the air for 2.4 seconds, it takes 1.2 seconds to rise to the top, when the vertical velocity is 0. Since the acceleration of gravity is 9.8 m/s, and you have v_vert(t) = v_vert_0 - gt, you have at 1.2 seconds: v = 0 = v_vert_0 - g(1.2) = 0, so v_vert_0 = 1.2g = 11.8 m/s. That will produce a height much bigger than 1.1 m.

Even if you ignore the value for t, you can compute the launch speed from :
- the launch angle and the maximum altitude.
- the launch angle and the horizontal range.
These are both pretty simple, but you get values for v that differ by 12%

Even after setting the launch angle at 45 degrees, the values are still inconsistent.
The inconsistency disappears if you don't assume the projectile lands at the same altitude it was launched from. e.g. It could be launched from a table and land on the floor.

O.P. Does the context of the problem allow for that possibility?