Kinematics question needed to be solved. Help please

[xrayxman]

Homework Statement

A basketball is being thrown at the hoop (3.0m high) from 4.0 meters away. If the initial height of the ball is at 1.5m with an initial velocity of 3.0 m/s, at what angle should the ball be thrown? (Assume that air resistance is zero, and gravity = 9.81 m/s^2)

Homework Equations

This is a kinematics problem. Even my teacher has trouble solving it. Please help. The main formulas are:

xf = x0 + Vx t + 1/2 a t^2

yf = y0 + Vy t + 1/2 a t^2

The Attempt at a Solution

By using the above two formulas, we came up with a quadratic equation involving tan() and cos() functions. We can't go further. Anyone suggestions?

12 tan(x) - 8.72(1/cos(x))^2 = 1.5

Let x be the starting angle of the ball being being thrown (above the horizontal)

Note: you can't just throw the ball to the hoop in a straight line, you will hit the hoop instead.

 

[grzz]

if you show how you got the equation someone can help you.

 

[Redbelly98]

Welcome to Physics Forums.

Homework Statement

A basketball is being thrown at the hoop (3.0m high) from 4.0 meters away. If the initial height of the ball is at 1.5m with an initial velocity of 3.0 m/s, at what angle should the ball be thrown? (Assume that air resistance is zero, and gravity = 9.81 m/s^2)

Homework Equations

This is a kinematics problem. Even my teacher has trouble solving it. Please help. The main formulas are:

xf = x0 + Vx t + 1/2 a t^2

yf = y0 + Vy t + 1/2 a t^2

Okay, but a would be zero in the xf equation.

The Attempt at a Solution

By using the above two formulas, we came up with a quadratic equation involving tan() and cos() functions. We can't go further. Anyone suggestions?

12 tan(x) - 8.72(1/cos(x))^2 = 1.5

I get almost the same thing, except that I have 4tan(x) instead of 12tan(x).

Let x be the starting angle of the ball being being thrown (above the horizontal)

Note: you can't just throw the ball to the hoop in a straight line, you will hit the hoop instead.

It's probably easiest to use a graphing calculator to solve the equation at this point. You only need to consider x between 0° and 90°, of course.