Kinematic Issues

Oblique movement

1. During a football match, a goalkeeper kicks a ball with a starting speed equal to 25m / s, forming a 45 ° angle with the horizontal. How far will the ball reach?

2. A cannon shot is fired at an angle of 30 ° to the horizontal as shown below:

, but when the height is maximum the final speed will be zero:

So the height the cannon shot reaches is 50m + 30m = 80m

3. Suppose you need to throw a book from the second floor of a building to a friend who is 10 meters away from you. What should be the initial speed with which you should launch it? Knowing that you will launch vertically and that the second floor window is 4 meters high from the ground.

Circular motion

1. The hands of the watch perform a uniform circular movement. What is the angular velocity of hands (a) of hours, (b) minutes (c) and seconds?

(a) The hour hand completes one turn (2π) in 12 hours (12 ∙ 3600s)

ωh = ∆φt

ωh = 2π12 ∙ 3600 = 1.45 ∙ 10-4 rad / s

(b) The minute hand completes one turn (2π) in one hour (3600s)

ωm = ∆φt

ωm = 2π3600 = 1.74 ∙ 10-3 rad / s

(c) The second hand completes one turn (2π) in one minute (60s)

ωs = ∆φt

ωs = 2π60 = 0.105 rad / s

2. If we consider a clock in the previous exercise, with a 10cm hour hand, 15cm minute hand and 20cm second hand. What will be the centripetal acceleration of each of the hands?

The first step to resolution is to transform the requested linear velocity into angular velocity.



3. A wheel of 1 meter in diameter, starting from rest, begins to turn with angular acceleration equal to 2rad / s². How long does it take to reach a linear speed of 20m / s?

The first step to resolution is to transform the requested linear velocity into angular velocity, considering that the wheel radius equals half the diameter. So:

From there, only the angular velocity hourly function applies:

4. A billiard ball, with a radius of 2.5cm, after being hit by the player, begins to spin with an angular velocity of 5rad / s, and decelerates to -1rad / s² until it stops, how much space does the ball travel? ?