Question

A football quarterback shows off his skill by throwing a pass 45.70 m downfield and into a bucket. The quarterback consistently launches the ball at 38.00 ∘ above horizontal, and the bucket is placed at the same level from which the ball is thrown.
What initial speed is needed so that the ball lands in the bucket? I got 21.5 m

By how much would the launch speed have to be increased if the bucket is moved to 48.70 m downfield?

Answer 1

Answer on Question #70476-Physics-Other

A football quarterback shows off his skill by throwing a pass 45.70 m downfield and into a bucket. The quarterback consistently launches the ball at 38.00 ♦ above horizontal, and the bucket is placed at the same level from which the ball is thrown.

What initial speed is needed so that the ball lands in the bucket? I got 21.5 m

By how much would the launch speed have to be increased if the bucket is moved to 48.70 m downfield?

Solution

Formula for the range of projectile is

$$x = \frac {v _ {0} ^ {2} \sin 2 \theta}{g}$$

The initial speed is

$$v _ {0} = \sqrt {\frac {g x}{\sin 2 \theta}} = \sqrt {\frac {(9 . 8 1) (4 5 . 7)}{\sin 2 (3 8)}} = 2 1. 5 \frac {m}{s}.$$

New speed is

$$v _ {0} ^ {\prime} = \sqrt {\frac {g x ^ {\prime}}{\sin 2 \theta}} = \sqrt {\frac {(9 . 8 1) (4 8 . 7)}{\sin 2 (3 8)}} = 2 2. 2 \frac {m}{s}.$$

The increase in speed is

$$v _ {0} ^ {\prime} - v _ {0} = 2 2. 2 - 2 1. 5 = 0. 7 \frac {m}{s}.$$

Answer provided by https://www.AssignmentExpert.com