The height to which the frog-hopper jumps on the surface of titan will be
and the range of the frog-hopper will be
.
Explanation:
The motion of the projectile on the surface of the planet occurs in two dimension. The vertical motion of the frog-hopper will be under the action of the gravity whereas the horizontal motion of the frog-hopper will be the motion under constant speed.
Write the expression for the maximum height attained by the frog-hopper:
...... (1)
Here,
is the maximum height attained by the frog-hopper,
is the velocity in vertical direction.
Consider that the height attained by the frog-hopper on the surface of titan is
and
on the surface of Earth.
Compare the maximum heights attained by the frog-hopper on Earth and titan:

Substitute the value of the acceleration due to gravity on each surfaces.

Write the expression for the range of jump of the frog-hopper:
...... (2)
Compare the range of the frog-hopper on the surface of Earth and titan:

Substitute the value of the acceleration due to gravity on each surfaces.

Thus, the height to which the frog-hopper jumps on the surface of titan will be
and the range of the frog-hopper will be
.
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Projectile motion
Keywords:
froghopper, tiny insect, titan, range, maximum height, vertical direction, projectile, in terms of h and r, takeoff velocity, raised a colony.