A ball is thrown up solve for variables, kenimatics

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The discussion centers on solving kinematic equations for a ball thrown from level ground at an initial speed \( v_0 \) and various angles \( \theta \). The key relationship derived is the ratio of the minimum speed \( v_{min} \) to the initial speed \( v_0 \), expressed as \( \frac{v_{min}}{v_0} = \cos(\theta) \). However, this response was not accepted by the computer system, indicating a need for a more comprehensive formula involving time of flight \( t \), maximum time of flight \( t_{max} \), and gravitational acceleration \( g \). The discussion suggests breaking the problem into two parts: vertical motion and horizontal motion.

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A ball is to be shot from level ground with a certain speed v0 at various angles θ. The launch angle determines both the time of flight t and the minimum speed vmin the ball will have during its flight, which means they can be related to each other. At some angle, the ball will have a maximum possible time of flight. Call this time tmax. Find a formula which gives the ratio of vmin to v0 in terms of t, tmax, and g.


I honestly do not know where to go with this one, it has stumped my roommate and i for over an hour!


It is asking for the answer in a ratio of vmin/v0

if simplified you can get an answer of vmin/v0 = v0 cos(theta)/v0 = cos(theta)

The computer does not accept this as a valid response.

Any help is appreciated,
Cheers!
 
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You need to read the book and think of how the example problems in kinematics relates to this.

Break it into two parts the ball motion going up and then coming down and the motion of the ball going horizontally.
 

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