A block is shot up a frictionless 40 degree slop with initial velocity v. It rea

Question

A block is shot up a frictionless 40 degree slop with initial velocity v. It reaches height "h" before sliding back down. The same is shot with the same velocity up a frictionless 20 degree slop. On this slope the block reaches height A) 2h B) h C) 1/2 h D) Greater than h but can't predict an exact value E) less than h but can't predict an exact value.
A block is shot up a frictionless 40 degree slop with initial velocity v. It reaches height "h" before sliding back down. The same is shot with the same velocity up a frictionless 20 degree slop. On this slope the block reaches height A) 2h B) h C) 1/2 h D) Greater than h but can't predict an exact value E) less than h but can't predict an exact value.
A block is shot up a frictionless 40 degree slop with initial velocity v. It reaches height "h" before sliding back down. The same is shot with the same velocity up a frictionless 20 degree slop. On this slope the block reaches height A) 2h B) h C) 1/2 h D) Greater than h but can't predict an exact value E) less than h but can't predict an exact value.
A) 2h B) h C) 1/2 h D) Greater than h but can't predict an exact value E) less than h but can't predict an exact value.

Explanation / Answer

the height is calculated as follows:

   s = v2/2gsin40

but, sin 40 = h/s

   s = h/sin40

then, the height is,

   h/sin40 = v2/2gsin40

then, the height is,

h = v2/2g

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the height is calculated as follows:

   s = v2/2gsin20

but, sin 20 = h/s

   s = h/sin20

then, the height is,

   h/sin20 = v2/2gsin20

then, the height is,

h = v2/2g

hence, it reaches height h.

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