A grasshopper hops along a level road. on each hop, the grasshopper launches itself itself at an angle of 45 degrees. and achieves a range of 0.77 m. what is the average horizontal speed of the grasshopper as it hops along the road? assume that the time spent on the ground between hops is negligible.

Question

Physics

Jayden Gentry

21 October, 00:53

A grasshopper hops along a level road. on each hop, the grasshopper launches itself itself at an angle of 45 degrees. and achieves a range of 0.77 m. what is the average horizontal speed of the grasshopper as it hops along the road? assume that the time spent on the ground between hops is negligible.

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Answers (1)

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Kamryn Reilly · Answer 1

Below is the solution:

R = v^2 sn (2θ) / g

v = [R g / sin (2θ) ]^1/2

vx = v cosθ = cosθ [R g / sin (2θ) ]^1/2

θ = π/4

then

vx = cos (π/4) [R g / sin (π/2) ]^1/2 = cos (π/4) (R g) ^1/2

vx = cos45 * (0.82*9.8) ^1/2

vx = 2 m/s