4.3 Projectile motion  (Page 9/13)

An athlete can jump a distance of 8.0 m in the broad jump. What is the maximum distance the athlete can jump on the Moon, where the gravitational acceleration is one-sixth that of Earth?

The maximum horizontal distance a boy can throw a ball is 50 m. Assume he can throw with the same initial speed at all angles. How high does he throw the ball when he throws it straight upward?

A rock is thrown off a cliff at an angle of $53\text{°}$ with respect to the horizontal. The cliff is 100 m high. The initial speed of the rock is 30 m/s. (a) How high above the edge of the cliff does the rock rise? (b) How far has it moved horizontally when it is at maximum altitude? (c) How long after the release does it hit the ground? (d) What is the range of the rock? (e) What are the horizontal and vertical positions of the rock relative to the edge of the cliff at t = 2.0 s, t = 4.0 s, and t = 6.0 s?

Trying to escape his pursuers, a secret agent skis off a slope inclined at $30\text{°}$ below the horizontal at 60 km/h. To survive and land on the snow 100 m below, he must clear a gorge 60 m wide. Does he make it? Ignore air resistance.

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of $40\text{°}$ with an initial speed of 20 m/s, how close to the green does she come?

A projectile is shot at a hill, the base of which is 300 m away. The projectile is shot at $60\text{°}$ above the horizontal with an initial speed of 75 m/s. The hill can be approximated by a plane sloped at $20\text{°}$ to the horizontal. Relative to the coordinate system shown in the following figure, the equation of this straight line is $y=(\text{tan}20\text{°})x-109.$ Where on the hill does the projectile land?

An astronaut on Mars kicks a soccer ball at an angle of $45\text{°}$ with an initial velocity of 15 m/s. If the acceleration of gravity on Mars is 3.7 m/s, (a) what is the range of the soccer kick on a flat surface? (b) What would be the range of the same kick on the Moon, where gravity is one-sixth that of Earth?

Mike Powell holds the record for the long jump of 8.95 m, established in 1991. If he left the ground at an angle of $15\text{°},$ what was his initial speed?

MIT’s robot cheetah can jump over obstacles 46 cm high and has speed of 12.0 km/h. (a) If the robot launches itself at an angle of $60\text{°}$ at this speed, what is its maximum height? (b) What would the launch angle have to be to reach a height of 46 cm?

Mt. Asama, Japan, is an active volcano. In 2009, an eruption threw solid volcanic rocks that landed 1 km horizontally from the crater. If the volcanic rocks were launched at an angle of $40\text{°}$ with respect to the horizontal and landed 900 m below the crater, (a) what would be their initial velocity and (b) what is their time of flight?

Drew Brees of the New Orleans Saints can throw a football 23.0 m/s (50 mph). If he angles the throw at $10\text{°}$ from the horizontal, what distance does it go if it is to be caught at the same elevation as it was thrown?

The Lunar Roving Vehicle used in NASA’s late Apollo missions reached an unofficial lunar land speed of 5.0 m/s by astronaut Eugene Cernan. If the rover was moving at this speed on a flat lunar surface and hit a small bump that projected it off the surface at an angle of $20\text{°},$ how long would it be “airborne” on the Moon?

A soccer goal is 2.44 m high. A player kicks the ball at a distance 10 m from the goal at an angle of $25\text{°}.$ What is the initial speed of the soccer ball?

Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what initial velocity would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of $3.7\text{m}\text{/}{\text{s}}^2.$

In 1999, Robbie Knievel was the first to jump the Grand Canyon on a motorcycle. At a narrow part of the canyon (69.0 m wide) and traveling 35.8 m/s off the takeoff ramp, he reached the other side. What was his launch angle?

You throw a baseball at an initial speed of 15.0 m/s at an angle of $30\text{°}$ with respect to the horizontal. What would the ball’s initial speed have to be at $30\text{°}$ on a planet that has twice the acceleration of gravity as Earth to achieve the same range? Consider launch and impact on a horizontal surface.

Aaron Rogers throws a football at 20.0 m/s to his wide receiver, who runs straight down the field at 9.4 m/s for 20.0 m. If Aaron throws the football when the wide receiver has reached 10.0 m, what angle does Aaron have to launch the ball so the receiver catches it at the 20.0 m mark?