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.