Question

Rank the following from lowest to highest vertical height all with initial velocity of 80 m/s: 31, 89 °, 17, 49 ", 41 °, 78

Answer 1

Ranking:

326.4 m, 312.4 m, 186 m, 140.5 m, 86.6 m, 27.9 m

Step-by-step explanation:

Projectile Motion

It's known as the type of motion that experiences an object that is launched near the Earth's surface and moves along a curved path exclusively under the action of gravity.

Being vo the initial speed of the object, θ the initial launch angle, and g=9.8m/s^2 the acceleration of gravity, then the maximum vertical height the object reaches is calculated by:

`\displaystyle h_m=(v_o^2\sin^2\theta)/(2g)`

We have to test for different launching angles and sort the maximum heights from lowest to highest. For all the test cases, vo=80 m/s.

• For θ=31°

`\displaystyle h_m=(80^2\sin^2 31^\circ)/(2\cdot 9.8)`

h=86.6 m

• For θ=89°

`\displaystyle h_m=(80^2\sin^2 89^\circ)/(2\cdot 9.8)`

h=326.4 m

• For θ=17°

`\displaystyle h_m=(80^2\sin^2 17^\circ)/(2\cdot 9.8)`

h=27.9 m

• For θ=49°

`\displaystyle h_m=(80^2\sin^2 49^\circ)/(2\cdot 9.8)`

h=186 m

• For θ=41°

`\displaystyle h_m=(80^2\sin^2 41^\circ)/(2\cdot 9.8)`

h=140.5 m

• For θ=78°

`\displaystyle h_m=(80^2\sin^2 78^\circ)/(2\cdot 9.8)`

h=312.4 m

Ranking:

326.4 m, 312.4 m, 186 m, 140.5 m, 86.6 m, 27.9 m