1. The problem statement, all variables and given/known data A grasshoopper jumps 1.00 m from rest, with an initial velocity at a 45.0 degree angle with respect to the horizontal. Find the initial speed of the grasshopper (answer is 3.13 m/s) The maximum height reached (answer is .250m) 2. Relevant equations acceleration in the x direction is considered constant, so you are using the basic kinematic equations, with a simplified equations for x vector components, e.g. V0x=cos(0) 3. The attempt at a solution The problem is that I can't figure out what they are asking. For example, up until now, in the class we have described an object at rest to have an initial velocity of zero. The question itself seems somewhat contradictory to me. What am I missing?
Velocity in x direction is considered constant. Velocity in y direction is changing due to gravity. You just need to find the components, and then, using basic kinematic equations, find maximum height, distance, initial velocity, time... Take a look at this.
It's just an oddly phrased question. Despite the use of "from rest", they don't intend for the grasshopper to have an initial velocity of zero when he jumps. He was "at rest" sometime before he jumped. A better phrasing would be something like: "A grasshopper jumps 1.00 m from its initial position, with an initial velocity at a 45.0 degree angle with respect to the horizontal."