Question

At an instant when a soccer ball is in contact with the foot of the player kicking it, the horizontal or x component of the ball's acceleration is 950 m/s2 and the vertical or y component of its acceleration is 750 m/s2. The ball's mass is 0.35 kg. What is the magnitude of the net force acting on the soccer ball at this instant?

Answer 1

F = 423.63 N

Step-by-step explanation:

Since, the x-component and y-components of the acceleration of ball are given. Therefore, we need to find the resultant or net acceleration of the soccer ball first. For that purpose we use to the formula for the resultant of rectangular components of a vector:

a = √(ax² + ay²)

where,

a = net acceleration = ?

ax = x - component of acceleration = 950 m/s²

ay = y - component of acceleration = 750 m/s²

Therefore,

a = √[(950 m/s²)² + (750 m/s²)²]

a = 1210.4 m/s²

Now, from Newton's Second Law, we know that:

F = ma

where,

m = mass of ball = 0.35 kg

F = Net force acting on ball = ?

F = (0.35 kg)(1210.4 m/s²)

F = 423.63 N