(Solved) How would I calculate the range of projectile for this equation:?

rinadtartir

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11 years ago

How would I calculate the range of projectile for this equation:?

im stuck with revision, how would I calculate the range of projectile , with velocity being 7.5 ms at and angle of 56 degrees, how would i work this out?? ive got the equation but struggled finding the right symbols to put it here! Any help would be great.

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Smileyriley20

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11 years ago

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Fezenius

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11 years ago

If you have an equation for the height of the projectile as a function of time, solve that equation for the times at which the height is zero. The largest value of that solution is the time at which the projectile impacts the ground. Determine the horizontal velocity of the projectile (muzzle velocity times the cosine of the elevation angle) and multiply that velocity by the time to impact. The result is the range or distance to impact.

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rimrod75

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11 years ago

DIvide the velocity into vertical and horizontal components

vy = 7.5 sin (56)
vx = 7.5 cos(56)

First figure out how long the project can stay in the air based on the vertical position equation

h(t) = 7.5 sin(56) t - .5(9.8)t^2

Here I'm using 9.8 for the accelleration due to gravity. Solve this equation for when h(t) is 0.
This will happen when t = 0, which we don't care about. You want the other t, which is the
time it hits the ground coming back down.

t = 7.5 sin(56)/(.5(9.8))

Knowing this you can figure out how far it goes in the horizontal direction

s(t) = 7.5cos(56)t Just plug in the t value you got above.

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