Hello my name is Stephanie and I have this problem forhomework and can\'t figure

Question

Hello my name is Stephanie and I have this problem forhomework and can't figure out which formula to use on these. Pleasehelp, thanks.
Superman leaps into the air with a speed of 45m/s in adirection 45 degrees above the horizontal. What are the componentsof his intial velocity in the x-and y-directions? How long does ittake him to reach the top of his trajectory? sschul5@comcast.net Hello my name is Stephanie and I have this problem forhomework and can't figure out which formula to use on these. Pleasehelp, thanks.
Superman leaps into the air with a speed of 45m/s in adirection 45 degrees above the horizontal. What are the componentsof his intial velocity in the x-and y-directions? How long does ittake him to reach the top of his trajectory? sschul5@comcast.net

Explanation / Answer

Given V = 45 m/s, sin 45 = cos 45 = .707 Vy init = 45 * .707 = 31.82 m/sec
The equation of motion is S = 1/2 at2 + Vot + So We just figured Vo, and will define the ground as So = 0 sowe have this:
S = -9.8 * (1/2) t2 + 31.82 t : When on the ground, S = 0 and we expect two solutions tothis, 0 when he jumps, and some positive value of t when helands.
4.9 t = 31.82 => t = 6.494seconds.
The top of the trajectory is exactly 1/2 the total time =3.247 seconds

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