Given angle and distance traveled find initial velocity

In summary, the conversation discusses finding the initial velocity of a ball that was hit by a batter and cleared the outfield fence, disregarding air friction. The approach involved breaking down the problem into components using the formulas Vx=Vcos45 and Vy=Vsin45, and setting up equations to solve for the unknowns. Simplification was also done by dividing one equation by t, and the problem ultimately came down to solving two equations with two unknowns.
  • #1
shaunk
2
0
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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  • #2
How did you approach the problem?
 
  • #3
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
 
  • #4
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
 

1. What is the formula for finding initial velocity given angle and distance traveled?

The formula for finding initial velocity given angle and distance traveled is: V0 = d / (t * sinθ), where V0 is the initial velocity, d is the distance traveled, t is the time taken, and θ is the angle of launch.

2. How do you find the angle of launch in this formula?

The angle of launch, θ, can be found using trigonometric functions. For example, if the projectile is fired at an angle of 30 degrees, then sin30° = 0.5. So, θ = sin-1(d / (V0 * t)).

3. Can this formula be used for all types of projectiles?

Yes, this formula can be used for all types of projectiles as long as the initial velocity and angle of launch are known. It is applicable for both horizontal and angled launches.

4. What units should be used for the variables in this formula?

The distance traveled, d, should be in meters (m), time taken, t, should be in seconds (s), and the initial velocity, V0, should be in meters per second (m/s). The angle of launch, θ, is measured in degrees (°) or radians (rad).

5. How does air resistance affect the accuracy of this formula?

This formula assumes that there is no air resistance. In reality, air resistance can affect the projectile's trajectory and therefore, the accuracy of this formula. However, it can still provide a close estimate of the initial velocity for most cases.

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