How do I solve this problem without time?

Who,me?

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.

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Andrew Mason
Homework Helper

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

Who,me?
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
$$v_o^2 = Rg/sin(2\theta)$$