An object is launched upward from the ground with an initial velocity of 40 feet per second. After how many seconds does the object reach a height of 25 feet?

Question

The question is really hard and I need help its for a summer pack for algebra 2. Please help me. I don't know how to do this but I hav taken algebra and geometry already so think if someone were to tell me what to do then I would be able to do it. 

Answer 1

I believe this question needs some hints from physics. I would think the text has some hints in the form of energy equations or kinematic equations.

 

The object is initially at a velocity v_i = 40 ft/sec, but instantly starts decelerating a = -32.2 ft/s/s or ft/s² due to gravity (g).

 

We don't know the final velocity (v_f) or the time (t) that has passed when it reach that velocity but we do know the height d = 25 ft.

 

From kinematic equations we know that:

 

 v_f² = v_i² + 2 * a * d and v_f = v_i + a * t

 

We have two equations and two unknowns. Solving the first equation gives you "v_f" which you can then use to solve for "t" in the second equation. I hope this helps. 

 

Hint: v_f² = (40 ft/s)² + 2 * -32.3 ft/s² * 25 ft solve for v_f. Note: the equation above has a v_f². 

 

Should be able to continue from here with some equation manipulation to solve for t.