Question

question 4. during a football game, camila and ronak watch a professional quarterback throw a football to a teammate. the football has a mass of 0.40 kg. in order for the football to reach his teammate, he must throw it with a force of 11 n. this force would allow the ball to move toward his teammate at the most effective rate for the teammate to score points. camila and ronak decide they want to try to recreate the play in her own youth football game the next weekend. during the game, she is able throw a football with a mass of 0.35 kg with a force of 7 n. how would decreasing the mass of the football to 0.30 kg affect its acceleration? a. it would increase the footballs acceleration to 3.85 m/s². b. it would have no effect on the acceleration of the football. c. it would decrease the footballs acceleration to 0.042 m/s². d. it would increase the footballs acceleration to 23.3 m/s².

Explanation:

Step1: Recall Newton's second - law formula

$F = ma$, where $F$ is force, $m$ is mass, and $a$ is acceleration. We assume the force remains the same as in Camila's throw ($F = 7N$).

Step2: Calculate the acceleration when $m = 0.30kg$

We can re - arrange the formula to $a=\frac{F}{m}$. Substitute $F = 7N$ and $m = 0.30kg$ into the formula: $a=\frac{7}{0.30}\approx23.3m/s^{2}$. When the mass was $0.35kg$, the acceleration was $a_1=\frac{7}{0.35}=20m/s^{2}$. Decreasing the mass from $0.35kg$ to $0.30kg$ increases the acceleration.

Answer:

D. It would increase the football's acceleration to 23.3 m/s²