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A dolphin in an aquatic show jumps straight up out of the water at a velocity of 15 m/s.
A: How long is the dolphin in the air in seconds? Neglect any effects due to his size or orientation.
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- 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 P3.19. (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?(a) If a person can jump a maximum horizontal distance (by using a 45 projection angle) of 3.0 m on Earth, what would be his maximum range on the Moon, where the free-fall acceleration is g/6 and g = 9.80 m/s2? (b) Repeat for Mars, where the acceleration due to gravity is 0.38g.Soba shot an arrow directly up in the air with a velocity of 60.0 [m/s]. Disregarding air resistance, A. What is the maximum height reached by the arrow? B. How long will the arrow stay in the air? After some time, Soba shoots a second arrow directly up in the air so that both arrows collide once the second arrow reaches a maximum height of 46.0 [m]. C. What should be the initial velocity of the second arrow? D. How long after shooting the first arrow should the second one be launched?
- A hot air balloon flying horizontally at a velocity of 50m/s and at an altitude of 475 meters when one if its sandbags falls off. A. How long (in seconds) does it take the sand bags to reach the ground? B. What horizontal distance (in meters) will the bag travel before it strikes the ground?A rocket leaves its platform with acceleration ⃗ a= ( 4.00 ^i+2.00 ^j ) m/s2 and initialvelocity v0= ( 8.00 ^i+12.0 ^j ) m/s for 5.00 seconds. After this 5.00 second interval, the rocket’sengines are turned off, and the rocket then travels as a projectile.a. Determine how long the rocket is in the air.b. What is the rocket’s velocity vector (in unit-vector notation) just before it hits theground?Suppose that a ball is thrown straight up in the air, and that a secondball is thrown straight upward two seconds after the first. It reaches thesame maximum height as the first ball.a. What is the position of the first ball as a function of time, y1(t)?Take the initial height of the ball as y0 = 0.b. What is the position of the second ball as a function of time, y2(t)?Take the initial height of the ball as y0 = 0.c. Draw a y − t diagram of y1(t) and y2(t). Label the max heights, timeto max height for the first ball, and note the point corresponding to thetime and height of passing.d. When do the balls pass each other in the air? Assume the balls arebeing throw up adjacent to each other.e. At what height above y0 = 0 do the balls pass each other?f. Can you find the time of passing by just using the y − t diagram?
- The height (in meters) of a projectile shot vertically upward from a point 2m above ground level with an initial velocity of 24.5 m/s is h = 2 + 24.5t - 4.9t2 after t seconds. a. When does the projectile reach its maximum height? b. What is the maximum height?A bullet is shot horizontally over level ground. The initial height is 1.3 m, and it’s initial speed is 241 m/s. a. How much time in seconds, elapses before the bullet hits the ground? b. How far does the bullet travel horizontally, in meters, before hitting the ground?5.e A water balloon is thrown upward from a window that is 80 meters high with an initial velocity of 25 meters per second. The function f(t) = -16t2 + 25t + 80 describes the height of the water balloon (in meters) at time t, measured in seconds from the initial release of the balloon. 1. What is the average velocity for the duration of the water balloon's flight? a. How much time elapsed from launch until impact? At = b. What is the displacement of the water balloon over this interval? Ay = Ay c. What was the average velocity during this interval? = Δt 2. What is the average velocity of the water balloon between t= 0.25 and t = 2? a. How much time elapsed? At = b. What is the displacement of the water balloon for this interval? Ay = Ay c. What was the average velocity for 0.25 < t< 2? At 3. What is the average velocity of the water balloon between t = 2.45 and t = 2.458? a. How much time elapsed? At = b. What is the displacement of the water balloon for this interval? Ay = Ay c. What…
- A long jumper leaves the ground at an angle of 20.0° to the horizontal and at a speed of 11.0 m/s. a. How long does it take for him to reach maximum height? b. What is the maximum height? c. How far does he jump? (Assume his motion is equivalent to that of a particle, disregarding the motion of his arms and legs.)A.Two motor vehicles, BMW and Ducati, are driving at SLEX southbound lane. At 9:00:00 am they are 100 meters apart and both having a velocity of 100 km/hr with BMW on the lead. The BMW suddenly decelerates at a constant rate of 5m/s while the Ducati retains its velocity. How much distance has the Ducati travelled from 9:00 am to the moment it starts to overtake the BMW? Express your answer in unit of meter. B.Two motor vehicles, BMW and Ducati, are driving at SLEX southbound lane. At 9:00:00 am they are 100 meters apart and both having a velocity of 100 km/hr with BMW on the lead. The BMW suddenly decelerates at a constant rate of 5m/s while the Ducati retains its velocity. What is the distance between both motor vehicles after 20s? Express your answer in unit of meter.Near the end of a marathon race, the first two runners are separated by a distance of 45.0 m. The front runner has a velocity of 3.50 m/s, and the second a velocity of 4.25 m/s. a. What is the velocity (in m/s) of the second runner relative to the first? b. If the front runner is 250 m from the finish line, who will win the race, assuming they run at constant velocity? c. What distance (in m) ahead will the winner be when she crosses the finish line?
