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

Bits

24 March, 06:12

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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Georgia Ochoa · 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