Ball thrown in air?

Question

A ball is thrown off a 23 m high cliff, at 4 m/s, 50 degrees above the horizontal. How long does it take to hit the ground?

Answer 1

maybe 30 mins or like 1/2 hours

Answer 2

For this problem, which is two-dimensional in nature, you must use the y-component properties of the motion. To find the total time, you must use the y-component of the velocity, the position function, and the quadratic formula.

The initial velocity (y-component) is:

vyi = vi sin θ = 4.00 m/s x sin(50.0°) = 3.06 m/s

The position function is:

yf = yi + vyi*t + ½*a*t²

- 23.0 m = 0 m + (3.06 m/s)*t  + (0.5 x (- 9.80 m/s²))*t²

0 = (- 4.50 m/s²)*t² + (3.06 m/s)*t + 23.0 m

Now use the quadratic formula to solve for the time:

0 = at² + bt + c

t = [ (- b) ± (b² - 4ac)^(1/2) ] / 2a

= [ - 3.06 ± ((3.06)² - (4 x -4.50 x 23))^(1/2) ] / (2 x -4.5)

= - 1.79 and 2.41

Time must be positive, therefore the answer is 2.41 s.