Solve Incline Problem: Find Highest Point Reached by Block

[milkyway11]

question says: a block is given an initial velocity of 2m/s up a frictionless plane inclined at 60 degree to the horizontal. what is the highest point reached by the block?

I tried to figure out how to solve the problem by thinking in order to find the highest point, i need the distance it traveled then I can use the sin to find the height. However, in order to find distance traveled, I will have to find the acceleration up the incline and this is where I get stuck. I tried to use kinematics to find the acceleration knowing final velocity will be 0, but I don't know the time spent traveling so I can't solve for acceleration!

Please help me solve it!

 

[Berko]

Use conservation of energy.

At the top, the kinetic energy is 0 so it is all potential energy. At the bottom, it is all kinetic (if you set V=0 at that point). The two values are equal...hence 1/2 mv^2 at bottom = mgh at top, but that h is the vertical height, so you need to use trigonometry to find the distance up the incline...

 

[Berko]

Of course, the acceleration (if you do not know the conservation of energy theorem) is easy enough to find. The only force acting down the block is the accelaration due to gravity (taking into account trigonometry to find it's component down the incline...)

 

[milkyway11]

thank you, this helps a lot!

Use conservation of energy.

At the top, the kinetic energy is 0 so it is all potential energy. At the bottom, it is all kinetic (if you set V=0 at that point). The two values are equal...hence 1/2 mv^2 at bottom = mgh at top, but that h is the vertical height, so you need to use trigonometry to find the distance up the incline...