How Is Time Calculated for a Ball Thrown Upwards?

[nk12]

A ball is thrown straight upward with a speed v from a point h metres above the ground. Express the time taken for the ball to strike the ground in terms of v,g and h.
(this question would be worth 4 marks on an assignment, so please answer according to the allocated marks) Thank you

 

[Jameson]

I'll first say that you should show some work because you're about to get pounced on for asking for answers.

Here's my tip... what kinematic equation(s) relate(s) the variables you mentioned?

 

[quicknote]

I understand the importance of expressing physical quantities in terms of relevant variables. In this case, we are looking to express the time taken for a ball to strike the ground in terms of its initial speed (v), acceleration due to gravity (g), and initial height (h).

To do this, we can use the equation of motion for a projectile in free fall, which is given by h = v*t - 1/2*g*t^2, where h is the height at time t, v is the initial velocity, and g is the acceleration due to gravity. In this case, we are interested in the time taken for the ball to reach the ground, so we can set h = 0, since the ball will have reached the ground at that point.

Solving for t, we get t = (v/g) * (1 + √(1 + 2*g*h/v^2)), which is the expression for the time taken for the ball to strike the ground. This equation takes into account the initial speed, acceleration due to gravity, and initial height of the ball.

In terms of marks, I would say this response would earn 4 marks because it provides a clear and concise expression for the time taken for the ball to strike the ground, taking into account all relevant variables. It also shows an understanding of the equation of motion for a projectile in free fall and how to apply it to this specific scenario.