Question

three arrows are shot at different angles into the air. arrow 1 is shot at 25° with a velocity of 16m/s, arrow 2 is shot upwards at an angle of 35° with a velocity of 14m/s, and arrow 3 is shot at an angle of 45° with a velocity of 10m/s. how does the vertical acceleration compare between arrow 1, arrow 2, and arrow 3?
(a) arrow 3 > arrow 2 > arrow 1
(b) arrow 1 > arrow 2 > arrow 3
(c) arrow 2 > arrow 1 > arrow 3
(d) arrow 3 = arrow 2 = arrow 1

Explanation:

Step1: Analyze the vertical acceleration of projectiles

When an object is in projectile motion near the Earth's surface, the only vertical force acting on it (neglecting air resistance) is the force of gravity. According to Newton's second law \(F = ma\), and the force of gravity \(F=mg\). So the vertical acceleration \(a_y\) is given by \(a_y=\frac{F_y}{m}\). Since \(F_y = mg\), then \(a_y=\frac{mg}{m}=g\). The value of \(g\approx - 9.8\ m/s^{2}\) (negative because it acts downwards) and is constant for all objects in projectile - motion near the Earth's surface, regardless of their initial velocity or launch angle.

Answer:

D. Arrow 3 = Arrow 2 = Arrow 1