Question

PROJECTILE MOTION

I don't know how to get started with this.

A grasshopper jumps a horizontal distance of 1m from rest, with an initial velocity at a 45 degree angle with respect to the horizontal. Find (a) the initial speed of the grasshopper and (b) the maximum height reached.

Answer 1

here we have to apply the formula of the range \(r\), namely:
\[r = \frac{{v_0^2}}{g}\sin \left( {2\theta } \right)\]

Answer 2

Where did you derive that from? Which kinematic equation?

Answer 3

that formula expresses the range \(r\) of an object, which is launched with a velocity whose magnitude \(v_0\) and angle (with respect to the horizontal line) equal to \(\theta\)

Answer 4

it is a standard formula, which can be derived from the theory of falling bodies

Answer 5

in our case we have: \(\theta=45\;degrees\)

Answer 6

from my formula above, we get:
\[{v_0} = \sqrt {\frac{{rg}}{{\sin \left( {2\theta } \right)}}} = \sqrt {\frac{{1 \cdot 9.81}}{{\sin \left( {2 \cdot 45} \right)}}} = ...m/\sec \]

Answer 7

I don't seem to understand that. We're only given three general equations.