Daring Darless wishes to cross the Grand Canyon of the Snake River by being shot from a cannon. She wishes to be launched at 65

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Daring Darless wishes to cross the Grand Canyon of the Snake River by being shot from a cannon. She wishes to be launched at 65

∘ relative to the horizontal so she can spend more time in the air waving to the crowd.
With what minimum speed must she be launched to cross the 520-m gap?
Express your answer to two significant figures and include the appropriate units.

Physics

1 answer:

ValentinkaMS [1.1K] · Answer 1 · 2026-03-04T14:21:28+03:00

Answer:

To successfully navigate the 520 m gap, she needs to be launched at a minimum speed of 57.67 m/s.

Step-by-step explanation:

Given:

The projectile's launch angle is, $\theta =65$ °

The range covered by the projectile is, $R=520$ m.

Gravity's acceleration is, $g=9.8\ m/s^2$

To determine the minimum speed necessary for crossing the gap, we use the formula related to the range of the projectile.

The projectile's range is calculated as:

$R=\frac{v_{0}^2\sin2\theta}{g}$

By substituting the provided values, we can find the minimum speed, $v_0$ .

$520=\frac{v_{0}^2\sin(2(65))}{9.8}\\520\times 9.8=v_{0}^2\sin(130)\\5096=1.532v_{0}^2\\v_0^2=\frac{5096}{1.532}\\v_0^2=3326.371\\v_0=\sqrt{3326.371}=57.67\textrm{ m/s}$

Thus, in order to clear the 520 m gap, she must be launched at a minimum speed of 57.67 m/s.