Can someone check my answers for the following questions. Thanks you.
1)A hockey puck's average velocity is 22 m/s. What is its displacement after 6.0s?
Answer: 132 m
2)It is 0.30 seconds after seeing a puff of smoke rise from the starter's pistol; the sound of firing the pistol is heard by the track timer 100 m away. What is the velocity of sound?
Answer: 333 m/s
3)The x- and y-components of a velocity vector of 100 N at 240 degrees would be:
Answer: -50 N,+86.6
4)A man pushes a lawn mower across the lawn exerting 5 N of force along the handle at an angle of 25 degrees with the ground. What is the x-component of the force he exerts?
Answer: 5.0
3) both the sin and cos of 240 are negative
4) cos 25 = .906
5 N cos 25 = 4.53 N
To check the answers for these questions, let's go through each one and explain how to arrive at the correct answers:
1) The average velocity is calculated by dividing the displacement by the time taken. In this case, the average velocity is given as 22 m/s, and the time is given as 6.0s. To find the displacement, we can rearrange the formula: displacement = average velocity x time. Plugging in the given values, we get: displacement = 22 m/s x 6.0s = 132 m. Therefore, the answer is correct.
2) The velocity of sound can be found by dividing the distance traveled by the time taken. In this case, the distance is given as 100 m, and the time taken is given as 0.30 seconds. So, velocity of sound = distance / time = 100 m / 0.30 s = 333.33 m/s (rounded to three decimal places). Hence, the provided answer of 333 m/s is correct.
3) To determine the components of a velocity vector given the magnitude and direction, we can use trigonometry. The given magnitude is 100 N, and the angle is 240 degrees. To find the x-component, we can use the formula: x-component = magnitude x cos(angle). Plugging in the values, we get: x-component = 100 N x cos(240 degrees) = -50 N (rounded to the nearest whole number). For the y-component, we can use the formula: y-component = magnitude x sin(angle). Plugging in the values, we get: y-component = 100 N x sin(240 degrees) = +86.6025404 N (rounded to three decimal places, as given in the answer).
4) To find the x-component of a force exerted at an angle, we can use trigonometry. The given force is 5 N, and the angle with the ground is 25 degrees. The x-component is given by: x-component = force x cos(angle). Plugging in the values, we get: x-component = 5 N x cos(25 degrees) = 4.558 m (rounded to one decimal place). Therefore, the given answer of 5.0 is incorrect.
To summarize the answers:
1) Displacement after 6.0 seconds = 132 m (correct)
2) Velocity of sound = 333 m/s (correct)
3) x-component = -50 N, y-component = +86.6 N (correct)
4) x-component of force = 4.6 N (not 5.0 N)