Range Equation: Launching a 78g Basketball at 8.4 m/s

[delfam]

Homework Statement

a 78g basketball is launched at 40.4 degrees at at 14.2m, ball is released at same height as basket. what speed must the player give the ball.

Homework Equations

deltax = 2(Vo^2)sin(2theta)

The Attempt at a Solution

14.2 = 2Vo^2 * (.9871360) / 9.8
69.58 = Vo^2(.9871360)
Vo^2 = 70.48
Vo = 8.4

 

[alphysicist]

Hi delfam,

Homework Statement

a 78g basketball is launched at 40.4 degrees at at 14.2m, ball is released at same height as basket. what speed must the player give the ball.

Homework Equations

deltax = 2(Vo^2)sin(2theta)

I don't believe this equation is quite right. What should it be?

The Attempt at a Solution

14.2 = 2Vo^2 * (.9871360) / 9.8
69.58 = Vo^2(.9871360)
Vo^2 = 70.48
Vo = 8.4

 

[delfam]

is it just (Vo^2) and not 2(Vo)^2

 

[jhae2.718]

Try solving for the general form of the range equation by taking
$$x(t)=v_0\cos(\theta)t \,\,\,\,(1)$$ and
$$y(t)=y_0+v_0\sin(\theta)t-\frac{gt^2}{2} \,\,\,\,(2)$$
solving (2) for the final time ($$t_f$$), and then substituting $$t_f$$ into (1) and simplifying.

Hint: your expression is missing a term from one of these equations.

 

[rwisz]

m/s

The range equation is a useful tool for calculating the distance an object will travel when launched at a certain velocity and angle. In this case, the 78g basketball is launched at 8.4 m/s and at an angle of 40.4 degrees. Using the range equation, we can calculate the distance the ball will travel, which is 14.2m in this scenario. However, the question asks for the speed the player must give the ball in order for it to reach this distance. Using the same equation, we can rearrange it to solve for the initial velocity (Vo) of the ball. Plugging in the given values, we get Vo = 8.4 m/s. Therefore, the player must give the ball an initial speed of 8.4 m/s in order for it to reach a distance of 14.2m at an angle of 40.4 degrees.