1) A kicker lines up to make a field goal attempt. If the ball leaves the kicker's foot at an initial speed of 20 m/s and an angle to the horizontal of 30.0°, a. Over what distances will the kick be successful (that it, over what range of distances will the ball clear the crossbar?) Assume the kick is in a domed stadium with no wind, and the ball is a point object.

1) A kicker lines up to make a field goal attempt. If the ball leaves the kicker's foot at an initial speed of 20 m/s and an angle to the horizontal of 30.0°, a. Over what distances will the kick be successful (that it, over what range of distances will the ball clear the crossbar?) Assume the kick is in a domed stadium with no wind, and the ball is a point object.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter4: Motion In Two And Three Dimensions

Section: Chapter Questions

Problem 100CP: When a field goal kicker kicks a football as hard as he can at 45 to the horizontal, the ball just...

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When a field goal kicker kicks a football as hard as he can at 45 to the horizontal, the ball just clears the 3-m- high crossbar of the goalposts 45.7 m away. (a) What is the maximum speed the kicker can impart to the football? (b) In addition to clearing the crossbar, the football must be high enough in the air early during its flight to clear the reach of the onrushing defensive lineman. If the lineman is 4.6 m away and has a vertical reach of 2.5 m, can he block the 45.7-m field goal attempt? (c) What if the lineman is 1.0 m away?
A projectile is launched with an initial speed of 60.0 m/s at an angle of 30.0 above the horizontal. The projectile lands on a hillside 4.00 s later. Neglect air friction, (a) What is the projectiles velocity at the highest point of its trajectory? (b) What is the straight-line distance from where the projectile was launched to where it hits its target?
A person standing at the top of a hemispherical rock of radius R kicks a ball (initially at rest on the top of the rock) to give it horizontal velocity vi as shown in Figure P3.56. (a) What must be its minimum initial speed if the ball is never to hit the rock after it is kicked? (b) With this initial speed, how far from the base of the rock does the ball hit the ground?
(a) A daredevil is attempting to jump his motorcycle over a line of buses parked end to end by driving up a 32° ramp at a speed of 40.0 m/s (144 km/h). How many buses can he clear if the top of the takeoff ramp is at the same height as the bus tops and the buses are 20.0 m long? (b) Discuss what your answer implies about the margin of error in this act—that is, consider how much greater the range is than the horizontal distance he must travel to miss the end of the last bus. (Neglect air resistance.)
In the blizzard of ’88, a rancher was forced to drop hay bales from an airplane to feed her cattle. The plane flew horizontally at 160 km/hr and dropped the bales from a height of 80 m above the flat range, (a) She wanted the bales of hay to land 30 m behind the cattle so as to not hit them. Where should she push the bales out of the airplane? (b) To not hit the cattle, what is the largest time error she could make while pushing the bales out of the airplane? Ignore air resistance.
Antlion larvae lie in wait for prey at the bottom of a conical pit about 5.0 cm deep and 3.8 cm in radius. When a small insect ventures into the pit, it slides to the bottom and is seized by the antlion. If the prey attempts to escape, the antlion rapidly launches grains of sand at the prey, either knocking it down or causing a small avalanche that returns the prey to the bottom of the pit. Suppose an antlion launches grains of sand at an angle of 72 above the horizon. Find the launch speed v0 required to hit a target at the top of the pit, 5.0 cm above and 3.8 cm to the right of the antlion.
A glider aircraft initially traveling due west at 85.0 km/h encounters a sudden gust of wind at 35.0 km/h directed toward the northeast (Fig. P3.62). What are the speed and direction of the glider relative to the ground during the wind gust? (The velocity of the glider with respect to the ground is the velocity of the gilder with respect to the wind plus the velocity of the wind with respect to the ground.)
A golfer hits his approach shot at an angle of 50.0, giving the ball an initial speed of 38.2 m/s (Fig. P4.60). The ball lands on the elevated green, 5.50 m above the initial position near the hole, and stops immediately. a. How much time passed while the ball was in the air? b. How far did the ball travel horizontally before landing? c. What was the peak height reached by the ball? FIGURE P4.60
A firefighter, a distance d from a burning building, directs a stream of water from a fire hose at angle i above the horizontal as shown in Figure P4.11. If the initial speed of the stream is vi, at what height h does the water strike the building? Figure P4.11
A strong softball player smacks the ball at a height of 0.7 m above home plate. The ball leaves the players bat at an elevation angle of 35 and travels toward a fence 2 m high and 60 m away in center field. What must the initial speed of the softball be to clear the center field fence? Ignore air resistance.
A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of vi = 18.0 m/s. The cliff is h = 50.0 m above a body of water as shown in Figure P4.13. (a) What are the coordinates of the initial position of the stone? (b) What are the components of the initial velocity of the stone? (c) What is the appropriate analysis model for the vertical motion of the stone? (d) What is the appropriate analysis model for the horizontal motion of the stone? (e) Write symbolic equations for the x and y components of the velocity of the stone as a function of time. (f) Write symbolic equations for the position of the stone as a function of time. (g) How long after being released does the stone strike the water below the cliff? (h) With what speed and angle of impact does the stone land? Figure P4.13
Sand is moving down a conveyor belt (with angle 15° from horizontal) at 6.0 m/s. You want the sand to enter a bucket that is 3.0 m below the end of the belt. How far in the horizontal directio, d, do you have to place the center of the bucket to ensure that the sand enters it?