A playground is on the flat roof of a city school, 6.00 m above the street below (Fig. P4.25). the vertical wall of the building is h 5 7.00 m high, forming a 1-m-high railing around the playground. A ball has fallen to the street below, and a passerby returns it by launching it at an angle of u 5 53.0° above the horizontal at a point d 5 24.0 m from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall.
(a) Find the speed at which the ball was launched.
(b) Find the vertical distance by which the ball clears the wall.
(c) Find the horizontal distance from the wall to the point on the roof where the ball lands.
When the ball is directly above the wall,
Hence, the speed at which the ball was launched came out to be .
Since the height of the wall is 7m
Therefore the ball clears the wall by
For first half of the trajectory,
For second half, solving for the final velocity,
Hence, the distance travelled in time
Therefore, the horizontal distance from the wall to the point of the roof where the ball lands is
24. Review. A student, along with her backpack on the floor next to her, are in an elevator that is accelerating upward with acceleration a. The student gives her backpack a quick kick at t = 0 , imparting to it speed v and causing it to slide across the elevator floor. At time t, the backpack hits the opposite wall a distance L away from the student. Find the coefficient of kinetic friction between the backpack and the elevator floor.
An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall when the floor drops away (Fig. P6.59). The coefficient of static friction between person and wall is , and the radius of the cylinder is . (a) Show that the maximum period of revolution necessary to keep the person from falling is . (b) If the rate of revolution of the cylinder is made to be somewhat larger, what happens to the magnitude of each one of the forces acting on the person? What happens in the motion of the person? (c) If the rate of revolution of the cylinder is instead made to be somewhat smaller, what happens to the magnitude of each one of the forces acting on the person? How does the motion of the person change?
Question: 51. A truck is moving with constant acceleration a up a hill that makes an angle with the horizontal as in Figure P6.51. A small sphere of mass m is suspended from the ceiling of the truck by a light cord. If Figure P6.51 the pendulum makes a constant angle θ with the perpendicular to the ceiling, what is a?
Question: 49. Interpret the graph in Figure 6.16 (b), which describes the results for falling coffee filters discussed in Example 6.10 . Proceed as follows. (a) Find the slope of the straight line, including its units. (b) From Equation 6.6 , identify the theoretical slope of a graph of resistive force versus squared speed. (c) Set the experimental and theoretical slopes equal to each other and proceed to calculate the drag coefficient of the filters. Model the cross-sectional area of the filters as that of a circle of radius 10.5 cm and take the density of air to be . (d) Arbitrarily choose the eighth data point on the graph and find its vertical separation from the line of best fit. Express this scatter as a percentage. (e) In a short paragraph, state what the graph demonstrates and compare it with the theoretical prediction. You will need to make reference to the quantities plotted on the axes, to the shape of the graph line, to the data points, and to the results of parts (c) and (d).
A particle on a spring moves in simple harmonic motion along the x axis between turning points at and . (i) At which of the following positions does the particle have maximum speed? (a) 100 cm (b) 110 cm (c) 120 cm (d) at none of those positions (ii) At which position does it have maximum acceleration? Choose from the same possibilities as in part (i). (iii) At which position is the greatest net force exerted on the particle? Choose from the same possibilities as in part (i).
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