19. A kangaroo can vertically jump over an object 2.5m high. A. What is its initial vertical speed to reach this height? B. How long will it stay in the air if it is jump- ing on a level ground? 20.Calculate the magnitude of the acceleration of a particle moving in a circle of radius r=0.5 m with a constant speed of 10m/s 21. A 0.525 kg ball is attached to a 1.25 m string and swings in a circular path making 2.00 revolutions per second. The angle of the string is nearly horizontal. Find the tension in the string. 22. A 0.525 kg ball is attached to a 1.25 m string and swings in a circular path . The angle of the string away from vertical is 30.0^circ Find the centripetal force acting on the ball and the speed of the ball.

Question

19. A kangaroo can vertically jump over an object 2.5m high. A. What is its initial vertical speed to reach this height? B. How long will it stay in the air if it is jump- ing on a level ground? 20.Calculate the magnitude of the acceleration of a particle moving in a circle of radius r=0.5 m with a constant speed of 10m/s 21. A 0.525 kg ball is attached to a 1.25 m string and swings in a circular path making 2.00 revolutions per second. The angle of the string is nearly horizontal. Find the tension in the string. 22. A 0.525 kg ball is attached to a 1.25 m string and swings in a circular path . The angle of the string away from vertical is 30.0^circ Find the centripetal force acting on the ball and the speed of the ball.

Answer 1

Let's solve each question step by step.**Question 19A: What is the initial vertical speed to reach a height of 2.5 m?**To find the initial vertical speed (v0) needed to reach a height (h) of 2.5 m, we can use the kinematic equation for vertical motion under constant acceleration due to gravity (g = 9.8 m/s²):

At the maximum height, the final velocity (v) is 0 m/s, so we can rearrange the equation to solve for v0:

Now plug in the values for g and h:

**Answer for 19A:** The initial vertical speed to reach a height of 2.5 m is approximately 11.07 m/s.**Question 19B: How long will it stay in the air if it is jumping on level ground?**The time (t) the kangaroo stays in the air can be found by doubling the time it takes to reach the maximum height since the ascent and descent times are equal. We can use the following kinematic equation:

At the maximum height, v = 0 m/s, so we can solve for t:

Using the initial vertical speed (v0) we found in 19A:

Since this is the time to reach the maximum height, the total time in the air is twice this:

**Answer for 19B:** The kangaroo will stay in the air for approximately 2.26 seconds.**Question 20: Calculate the magnitude of the acceleration of a particle moving in a circle of radius r = 0.5 m with a constant speed of 10 m/s.**The formula for centripetal acceleration (ac) for an object moving in a circle at constant speed (v) is:

Plugging in the values for v and r:

**Answer for 20:** The magnitude of the acceleration is 200 m/s².**Question 21: Find the tension in the string.**The tension in the string (T) provides the centripetal force (Fc) necessary to keep the ball moving in a circle. The formula for centripetal force is:

where m is the mass of the ball and ac is the centripetal acceleration. The centripetal acceleration can be found using the formula:

However, we are not given the speed (v) directly, but we know the ball makes 2.00 revolutions per second (f). We can find the speed using the formula for the circumference of a circle (C = 2πr) and the frequency:

\( v = 2 \pi \cdot 1.25 \, \text{m} \cdot 2.