# Finding minimum V and angle given horizontal and vertical travel

## Homework Statement

a mountain climber plans to jump from A to B over a crevasse. Determine the smallest value of the climbers initial velocity Vo and the corresponding value of the angle alpha so he lands at B

## Homework Equations

A to B is 1.8m horizontal distance and B is lower than A by 1.4m
Xx=Vo*T
Xy=Vo*T-.5*9.81*t^2

## The Attempt at a Solution

Distance X = 1.8 = cos(alpha)*Vo*t => T=1.8/(cos(alpha)*Vo)
Distance Y = -1.4= Vo* (1.8/(cos(alpha)*Vo)-.5*9.81*(1.8/(cos(alpha)*Vo))^2

My question is I don't know what other equation to use since I have two unknown equations I thought I could use the Range equation R= (Vo^2/g)*Sin(2alpha) but this is not on level ground so I dont think it will work. Ideas?

• salma shatta

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should I put this in advanced? Im not sure.

Hi, im cant solve the same problem!

I did the same thing, wrote down the equation for position using unit vectors, then replaced T in Y position equation.

and simplified everything to

Y(t)= -1.4= Vo*sin(alpha)* (1.8/(cos(alpha)*Vo)-.5*32.1*(1.8/(cos(alpha)*Vo))^2

Y(t)= -1.4= 1.8Tan(alpha) -51.8*(1+tan^2 (alpha))/V^2