Knowing the total distance traveled, and angle of launch, how would you find the velocity?

Question

The total distance traveled by a ball launched at an angle of 15 degrees is approximately 1.38 meters. Not counting air friction, and the final velocity being zero, how would you find the velocity?

Answer 1

This looks like a projectile problem, but its final velocity is not zero, assuming by final you mean when it hits the ground.  You can use the range relation for a projectile to find its launch speed v₀.  If you launch it up from the ground at an angle θ and initial speed v₀, it travels a horizontal distance R, called the range, before it hits the ground.

 

R = v₀²sin(2θ) / g ⇒

 

v₀ = √[Rg / sin(2θ)]

 

R = 1.38 m

θ = 15°

2θ = 30°

g = 9.8 m/s²

 

v₀ = √[1.38(9.8) / sin(30°)] m/s ≅ 5.20 m/s