How do I solve this problem without time?

Homework Statement

A grasshopper jumps 1.00 m from rest, with an initial velocity at a 45.0 degree angle with respect to the horizontal. Find a. the initial speed of the grasshopper (the answer is 3.13 m/s) and b. the maximum height reached ( the answer is .250 meters).

Homework Equations

V naught of x= v naught (hyp. of v. vectors) times cos (projection angle)
It should all be derived from the basic mechanic equations;
V= vnaught times time + a times time
Delta x= vnaught times time + .5 a times time squared
v squared= v naught squared + 2a delta x
I suspect they want me to use the cosine and sine versions but I need the steps so I can truly understand what I'm looking for!

The Attempt at a Solution

I keep getting zero I don't understand

Can somebody please give me all the steps for this problem and what formulas to use if I don't have them. I can crunch the numbers but for some reason I have a mental block on this problem. I don't even get how if it starts at rest, it can have any other value but zero.

 

[Andrew Mason]

Homework Statement

A grasshopper jumps 1.00 m from rest, with an initial velocity at a 45.0 degree angle with respect to the horizontal. Find a. the initial speed of the grasshopper (the answer is 3.13 m/s) and b. the maximum height reached ( the answer is .250 meters).

Homework Equations

V naught of x= v naught (hyp. of v. vectors) times cos (projection angle)
It should all be derived from the basic mechanic equations;
V= vnaught times time + a times time
Delta x= vnaught times time + .5 a times time squared
v squared= v naught squared + 2a delta x
I suspect they want me to use the cosine and sine versions but I need the steps so I can truly understand what I'm looking for!

The Attempt at a Solution

I keep getting zero I don't understand

Can somebody please give me all the steps for this problem and what formulas to use if I don't have them. I can crunch the numbers but for some reason I have a mental block on this problem. I don't even get how if it starts at rest, it can have any other value but zero.

Write out the expression for v as a function of range R, and the angle. You have enough information to calculate it. see: http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra13

AM

 

That really doesn't help me. I can't find the range without at least the V naught of the y component and the range of both the x and y component velocity vectors. So, at halfway the velocity component in the x direction is 0 and the vertical component of that is the velocity of Y at .5 meters which still leads me back to the formula where I am without V naught of R. I really just need the steps because then I can work backwards, without them if I try to move on in the chapter without this knowledge it does me no good.

 

[Andrew Mason]

That really doesn't help me. I can't find the range without at least the V naught of the y component and the range of both the x and y component velocity vectors. So, at halfway the velocity component in the x direction is 0 and the vertical component of that is the velocity of Y at .5 meters which still leads me back to the formula where I am without V naught of R. I really just need the steps because then I can work backwards, without them if I try to move on in the chapter without this knowledge it does me no good.

It certainly does help you. Do you think you are expected to work out the relationship between range, angle and speed every time you have such a problem? You have the range, R. You have the angle. You know g. All you have to do is plug these values into the equation!

$$v_o^2 = Rg/sin(2\theta)$$

AM