The froghopper, Philaenus spumarius, holds the world record for insect jumps. When leaping at an angle of 58.0∘ above the horizontal, some of the tiny critters have reached a maximum height of 58.7 cm above the level ground. (a) What was the takeoff speed for such a leap? (b) What horizontal distance did the froghopper cover for this world-record leap?

a) v₀ = 4 m/s

b) Xmax = 1.467 m

Explanation:

Given

∅ = 58°

ymax = 58.7 cm = 0.587 m

a) v₀ = ?

We use the formula

ymax = (v₀*Sin ∅)²/(2g)

⇒   v₀ = √(2g*ymax)/Sin ∅ = √(2*(9.81 m/s²)*(0.587 m))/Sin 58°

⇒   v₀ = 4 m/s

b) We apply the equation

Xmax = v₀²*Sin (2∅)/g

⇒  Xmax = (4 m/s)²*Sin (2*58°)/(9.81 m/s²) = 1.467 m

b.transmitters send radio waves, and receivers capture radio waves.

gpe = mass x gravity constant x height or… gpe = mgh

where… mass: measured in kilograms (kg)

gravity: gravity constant on earth = 10.00 m/s2

height: measured in meters (m)

gpe: measured in joules (j) or kilojoules (kj)

how do you solve gpe?

gravitational potential energy (gpe) is the energy an object has because of its position above the. ground.

gpe = mass x gravity constant x height or… gpe = mgh.

mass:

note: to earn full marks when solving science word problems, you must show your work:

formula.

example:

given values:

mass = 0.3 kg.