Child sitting in a tree throws his apple from the height of 4.0 m with a velocity of 5.0 m/s [35 degrees above horizontal]. It hits the ground right next to his friend. How long is it before the apple core hits the ground?
For this question, you can use:
`dy= V_(iy) * t + 1/2at^2`
Now first we shall assign the values needed to solve for the time required.
`dy` = -4 (direction is down)
`V_iy` = 5m * sin (35) = 2.8679
`a ` = acceleration due to gravity = -9.81m/s^2 (direction is down)
`t ` = time = ?
By substitution, we can now have:
`-4 = 2.8679t - 4.9t^2`
Arranging the equation into standard form:
`4.9x^2 -2.8679x - 4 = 0`
To solve for the value of t, quadratic equation is used.
`x = (-b +-sqrt(b^2 - 4ac))/(2a)`
The two values derived from this equation are -0.657 and 1.24. we will choose the positive time which is 1.24 seconds.
Final answer: 1.24 ~ 1.2 seconds