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My problem goes :

A projectile is fired with initial speed v_0 at an angle of \alpha up a hill slope \beta (\alpha > \beta)

a) How far up the hill will the projectile land.

Attempt to solution:

I understood that this is a problem where I need to find the intersection of the parabola and the line.

the function of the line is y= x tan (\beta)

The parabola is y = [gx^2+2x(v_0)^2cos (\alpha)sin(\alpha) ]/ [ 2(v_0)^2 (\alpha)]

After making them equal to each other I get

x= [2 (v_0)^2 cos (\alpha) sin (\alpha- \Beta) ] / gcos (\beta)

This is almost the answer... but somewhere I made a mistake or I am missing an step. Is my approach correct?

P.S. The answer is d= [2 (v_0)^2 cos (\alpha) sin (\alpha- \Beta) ] / g cos^2 (\beta)

A projectile is fired with initial speed v_0 at an angle of \alpha up a hill slope \beta (\alpha > \beta)

a) How far up the hill will the projectile land.

Attempt to solution:

I understood that this is a problem where I need to find the intersection of the parabola and the line.

the function of the line is y= x tan (\beta)

The parabola is y = [gx^2+2x(v_0)^2cos (\alpha)sin(\alpha) ]/ [ 2(v_0)^2 (\alpha)]

After making them equal to each other I get

x= [2 (v_0)^2 cos (\alpha) sin (\alpha- \Beta) ] / gcos (\beta)

This is almost the answer... but somewhere I made a mistake or I am missing an step. Is my approach correct?

P.S. The answer is d= [2 (v_0)^2 cos (\alpha) sin (\alpha- \Beta) ] / g cos^2 (\beta)

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