Projectile Motion Arrow Problem

AI Thread Summary
The discussion focuses on solving a projectile motion problem involving an arrow shot at an angle of 31.0° with an initial velocity of 53 m/s. The key calculations involve determining the maximum height the arrow reaches and the horizontal distance to the target, which is at the same height as the launch point. The user attempts to find the maximum height using the formula Max Height = Vi*T + 1/2*-9.8*T^2 and calculates time (T) to reach maximum height as 2.18 seconds. The need for a kinematic equation that relates initial velocity, acceleration, and final velocity at maximum height is emphasized. The discussion highlights the importance of neglecting air resistance and correctly applying the principles of projectile motion.
davetheant
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An arrow is shot at 31.0° above the horizontal. Its velocity is 53 m/s, and it hits the target.
A) What is the maximum height the arrow will attain?
B) The target is at the height from which the arrow was shot. How far away is it?


It says to neglect air resistance so acceleration in the x direction must be 0. Obviously gravity makes the acceleration in the y direction -9.8

I tried to calculate the maximum height by using the formula Max Height = Vi*T+1/2*-9.8*T^2

I got T to equal 2.18 by [53*sin(40)]/9.8
please help
 
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In the first case, the initial velocity in the upward direction is known, acceleration is given and final velocity at the maximum height is known(?). Find the maximum height. Which kinematic equation relates all these quantities?
 

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