Projectile Motion Homework: Finding Initial Speed and Flight Time

AI Thread Summary
To find the initial speed of a bullet shot straight up to a maximum height of 612 m, the final velocity at the peak is 0 m/s. Using the kinematic equation that relates initial velocity, final velocity, acceleration, and displacement, the initial speed can be expressed as Vo = sqrt(2gh), where g is the acceleration due to gravity. The total flight time can be calculated using the expression t = 2Vo/g, which accounts for the ascent and descent of the bullet. The key is to recognize that the bullet's velocity is zero at its maximum height, allowing for the calculation of initial velocity. Understanding these relationships is crucial for solving projectile motion problems effectively.
kinslow31
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Homework Statement


A bullet is shot straight up into the air. It reaches a maximum height at h = 612 m.

Find an expression for the initial speed of the ball.

Using your previous results find a numeric time for the total flight time, t until the ball reaches the ground.

Homework Equations





The Attempt at a Solution




Ok so I am assuming at initial speed y is 0 although it seems like Vo would be zero there to but if i do i got Vot=(1/2)gt^2 Vo = (1/2)gt i think that's right for projectile motion, if it is the expression for t is = 2Vo/g because at that time y=yo=0, but now how do i get a numeric value for it i can't figure out Vo, initial velocity, is it just zero? I am pretty stuck here
 
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If the bullet had an initial muzzle velocity of 0 coming out of the gun, how high would it go?

You are given how high the bullet goes and that it is traveling straight up (against gravity). You also need to realize that the bullet's velocity at its highest point is 0. With that information in hand, you need to relate initial and final velocity to acceleration and distance - initial velocity should be your only unknown (which you can solve for).
 
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