Solving for Time: Launching a Ball at an Angle - Homework Solution

[Calpalned]

Homework Statement

A ball is launched from a height of 1.9m with a speed of 40 m/s at an angle of 10 degrees above the horizontal. Find the total time in the air.

Homework Equations

$y_f = y_0 + v_0y t + \frac{1}{2} t^2$

The Attempt at a Solution

Taking y₀ = 1.9 m and v₀ = 40sin(10), then using the quadratic formula, I got the answers t = 1.65 or t = -0.23. Clearly the former is what we need. However, my solutions guide got t = 3.3 instead (that is, double my answer). The solution guide used the equation $t = \frac{-v_0 sin(θ) - \sqrt{v_0^2 sin^2(θ) + 2gy_0}}{-\frac{1}{2}g}$ and got 3.3 seconds. Why is this the case?

 

[gneill]

They failed to multiply the coefficient of the squared term by 2 in the denominator. For the quadratic ax² + bx + c = 0, the quadratic formula puts "2a" in the denominator.