How Do You Solve Equations with Variables V, U, and T?

[g9WfI]

Homework Statement

A ball is thrown vertically upwards at 12m/s to dislodge a kite stuck in a tree 5m above the thrower. Calculate the time before the ball reaches the kite. Explain why this question has two solutions.

Relevant Equations

suvat

Hi,

I'm new to the forum so I'm not so sure if I've formatted this correctly :p

I don't really know where to start with the question above as there are three unknowns (v, u, and t).

Answer is 0.53s or 1.9s - I'm so grateful for any help.

Many thanks.

 

[Orodruin]

Welcome to PF! Now, as you are new, you may not be familiar with the homework guidelines, but according to those you will need to provide your own attempt at a solution before we can help you. ("I don't know" is not sufficient as an attempt.)

What makes you say that $u$ (the initial velocity) is unknown? It is given right there in the problem statement:

A ball is thrown vertically upwards at 12m/s

 

[g9WfI]

So sorry, I meant acceleration, final velocity and t are unknown.

On attempt, I assumed v = 0
Then used: s = ((u + v)/2) t
5 = 12/2 t
t = 0.83 s

 

[PeroK]

On attempt, I assumed v = 0

Why would you assume that?

 

[hmmm27]

You might start by asking yourself why there's two solutions. If the answer is "dunno", try again : this time thinking a kite which is just tissue-paper, and a very jagged, very fast upwards-moving rock. What happens ?

 

[haruspex]

So sorry, I meant acceleration, final velocity and t are unknown.

On attempt, I assumed v = 0
Then used: s = ((u + v)/2) t
5 = 12/2 t
t = 0.83 s

There are five SUVAT equations, each omitting one of those five variables.
Work out which three variables you are given, which you are trying to find, and use the equation that involves those four.

(There are more complicated situations where you need an equation for each of different parts of a motion, and one of the unknowns appears in both equations.)

 

[Orodruin]

acceleration, final velocity and t are unknown.

Presumably this all happens on the Earth.

 

[g9WfI]

Thank you all so much for your help. I've been able to work out the answer.

 

[kuruman]

You might start by asking yourself why there's two solutions. If the answer is "dunno", try again : this time thinking a kite which is just tissue-paper, and a very jagged, very fast upwards-moving rock. What happens ?

It could be what you say or it could be that the kite needs to be hit when the rock is on its way down rather than on its way up. If the delivered impulse is up, there is a good chance that the kite will be lifted up and fall back down to the same spot. If the rock is to rip the kite, it will do so regardless of its direction of motion because the speed is the same at that height.

 

[hmmm27]

It could be what you say or it could be that the kite needs to be hit when the rock is on its way down rather than on its way up. If the delivered impulse is up, there is a good chance that the kite will be lifted up and fall back down to the same spot. If the rock is to rip the kite, it will do so regardless of its direction of motion because the speed is the same at that height.

The "jagged rock" was (hopefully) a mild hint of why there's two solutions. Since the problem explicitly requires the student to explain why there's two solutions, simply giving the answer didn't seem appropriate.

Explain why this question has two solutions.

Answer is 0.53s or 1.9s

I haven't run the calc's myself, so can't really verify the book answer.

 

[PeroK]

It could be what you say or it could be that the kite needs to be hit when the rock is on its way down rather than on its way up. If the delivered impulse is up, there is a good chance that the kite will be lifted up and fall back down to the same spot. If the rock is to rip the kite, it will do so regardless of its direction of motion because the speed is the same at that height.

I would hope there was less chance of damaging the kite if you hit it on the way up.