An ace footballer converted a penalty shot by kicking the football with a speed of 108 km h⁻¹. The estimated force they imparted was 800 N. The mass of the football was 0.4 kg. Calculate the time of contact between their foot and the ball.
To calculate the time of contact between the footballer's foot and the ball, we first need to convert the given speed into standard SI units. The initial velocity (u) of the ball is 0 m/s since it was at rest, and the final velocity (v) is given as 108 km h⁻¹. Converting this to m s⁻¹: v = 108 × (5/18) = 30 m s⁻¹.
Next, we calculate the acceleration of the football using Newton's second law of motion. The formula is F = ma, where F is the force, m is the mass, and a is the acceleration. Rearranging for acceleration, we get a = F/m. Substituting the given values: a = 800 N / 0.4 kg = 2000 m s⁻².
Now, we use the kinematic equation v = u + at to find the time of contact (t). Substituting the known values into the equation: 30 m s⁻¹ = 0 m s⁻¹ + (2000 m s⁻² × t).
Solving for t, we get: 2000t = 30, which gives t = 30 / 2000 = 0.015 s. Therefore, the time of contact between the footballer's foot and the ball is 0.015 s.
Explanation
The problem requires converting the velocity to m/s, finding acceleration using Newton's second law (a=F/m), and then using the first equation of motion (v=u+at) to find the time of contact. The initial velocity is 0.
Solution Steps
Step 1: Convert speed to m/s: v = 108 × (5/18) = 30 m/s
Step 2: Calculate acceleration using F=ma: a = F/m = 800/0.4 = 2000 m/s²
Step 3: Use v = u + at to find time: 30 = 0 + 2000t
Step 4: Solve for t: t = 30/2000 = 0.015 s