a batman deflects a boy by an angle 90 without change in acc. speed of 54km/h if mass of ball is 0.15kg. what is the impulse exerted on the ball also find force exerted on ball if ball remain for 0.1sec In connected with wall?
To calculate the impulse exerted on the ball, we need to use the formula:
Impulse = change in momentum
The formula for momentum is:
Momentum = mass × velocity
Given:
Mass of the ball (m) = 0.15 kg
Initial velocity of the ball (u) = 54 km/h
First, we need to convert the velocity from km/h to m/s:
1 km/h = (1000 m) / (60 × 60 s) = 0.2778 m/s
So, the initial velocity of the ball (u) will be:
u = 54 × 0.2778 m/s = 15 m/s
Now, to find the final velocity of the ball (v), we need to use trigonometry.
The angle of deflection (θ) = 90 degrees
Since the angle of deflection is 90 degrees, the ball will reflect back in the opposite direction, so the final angle will also be 90 degrees.
This means, the final velocity (v) will have the same magnitude of 15 m/s but opposite direction.
Therefore, the change in velocity (Δv) will be:
Δv = v - u = -15 m/s - 15 m/s = -30 m/s
Now we can calculate the impulse exerted on the ball:
Impulse = change in momentum = mass × change in velocity
Impulse = 0.15 kg × (-30 m/s) = -4.5 kg·m/s (Note: It has a negative sign because the velocity changed in the opposite direction)
To find the force exerted on the ball, we can use the formula:
Force = Impulse / time
Given:
Time (t) = 0.1 s
Force = -4.5 kg·m/s / 0.1 s
Force = -45 N (Note: It has a negative sign as force is exerted opposite to the direction of motion of the ball)
Therefore, the impulse exerted on the ball is -4.5 kg·m/s, and the force exerted on the ball is -45 N.
To find the impulse exerted on the ball, we first need to calculate the change in velocity of the ball when it is deflected by the bat. Impulse is defined as the change in momentum of an object.
Given:
Angle of deflection (θ) = 90 degrees
Initial speed of the ball (u) = 54 km/h
Mass of the ball (m) = 0.15 kg
To calculate the change in velocity, we need to convert the initial speed from km/h to m/s:
Initial speed (u) = 54 km/h = (54 * 1000) m/ (3600) s = 15 m/s
Since there is no change in acceleration, we assume that the displacement along the direction of motion is zero. Therefore, the final velocity (v) after the deflection will have the same magnitude as the initial velocity but in the opposite direction.
Change in velocity (Δv) = -2u = -2 * 15 = -30 m/s
Impulse (I) is defined as the product of the force exerted on an object and the time interval for which the force is applied. To calculate the impulse, we need to find the force exerted on the ball.
Given:
Time interval (t) = 0.1 sec
Impulse (I) = Force (F) * Time interval (t)
Rearranging the formula, we can calculate the force exerted on the ball:
Force (F) = Impulse (I) / Time interval (t)
Now we can put the values into the formulas:
Impulse (I) = mass of the ball (m) * Change in velocity (Δv)
Impulse (I) = 0.15 kg * (-30 m/s) = -4.5 kg·m/s (Note: The negative sign indicates the change in direction)
Force (F) = -4.5 kg·m/s / 0.1 s = -45 N
Therefore, the impulse exerted on the ball is -4.5 kg·m/s, and the force exerted on the ball when it remains in contact with the wall for 0.1 seconds is -45 N.