Given angle and distance traveled find initial velocity

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Homework Help Overview

The problem involves determining the initial velocity of a ball hit at a 45-degree angle, which travels a distance of 98 meters to clear an outfield fence. The scenario assumes no air friction and that the height of the fence matches the pitch height.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss breaking down the problem into horizontal and vertical components of motion, using trigonometric relationships for velocity. There are attempts to set up equations based on the distance traveled and the effects of gravity.

Discussion Status

Some participants have provided equations derived from the components of motion, leading to a system of equations with two unknowns. There is an ongoing exploration of how to simplify and solve these equations without reaching a consensus on the next steps.

Contextual Notes

Assumptions include neglecting air resistance and that the height of the fence is equal to the height of the pitch. The discussion reflects uncertainty about the time variable in the equations.

shaunk
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A ball is pictched at a batter, the batter hits the ball at a 45 degree angle It just clears the outfield fence 98m away Find velocity of the ball when it left the bat. Assume fence is the same height as the pitch. Disreguarding air friction I can't figure out how to find initial velocity.
 
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How did you approach the problem?
 
I attempted to break the problem down to its components using Vx= Vcos45 and vy=Vsin45 then used the formula Vx=x/t then 0=Vyit = 1/2gt^2
 
shaunk said:
I attempted to break the problem down to its components using Vx= Vcos45 and vy=Vsin45 then used the formula Vx=x/t then 0=Vyit = 1/2gt^2

Looks good to me.

so

Vx*t = 90

Vcos45*t = 90
Vsin45*t - (1/2)gt^2 = 0

you've got 2 equations with 2 unknowns... you can simplify the second equation by dividing by t (since the answer we need is not t = 0)...

Vsin45 - (1/2)gt = 0

so solve:

Vcos45*t = 90
Vsin45 - (1/2)gt = 0
 

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