Question

In: Physics

Bob has just finished climbing a sheer cliff above a beach, and wants to figure out...

Bob has just finished climbing a sheer cliff above a beach, and wants to figure out how high he climbed. All he has to use, however, is a baseball, a stopwatch, and a friend on the ground below with a long measuring tape. Bob is a pitcher, and knows that the fastest he can throw the ball is about 33.7 m/s. Bob starts the stopwatch as he throws the ball (with no way to measure the ball\'s initial trajectory), and watches carefully. The ball rises and then falls, and after 0.910 seconds the ball is once again level with Bob. Bob can\'t see well enough to time when the ball hits the ground. Bob\'s friend then measures that the ball landed 125 m from the base of the cliff. How high up is Bob, if the ball started from exactly 2 m above the edge of the cliff?

Solutions

Expert Solution

Given that

The initial speed ofthe ball (u) =33.7m/s

The time of flight for the ball(t) =0.910s

Acceleration due to gravity (g) =9.81m/s2

The time for which the ball remained in the air along the tajectory is given by

t =2usintheta/g

Then angle with which it is projected is given by

sintheta =gt/2u

theta=sin-1(gt/2u) =sin-1(9.81*0.910/2*33.7) =7.61degrees

Now the horizontal component of velocity is given by

ux =ucosthea =(33.7)cos(7.61) =33.403m/s

and the vertical component is given by

uy =usintheta =(33.7)sin(7.61)=4.462m/s

Then the time taken for the ball to reach 125m from the projection is gvien by

x =ux*t

t =x/ux =125/33.403 =3.742s

How high up is Bob, if the ball started from exactly 2 m above the edge of the cliff is given by

y =uyt+(1/2)at2

y =-(4.462)(3.742)-0.5(9.81)(3.742)2=-85.372m

How high up is Bob, if the ball started from exactly 2 m above the edge of the cliff is =85.372-2m =83.372m


Related Solutions

Bob has just finished climbing a sheer cliff above a beach, and wants to figure out...
Bob has just finished climbing a sheer cliff above a beach, and wants to figure out how high he climbed. All he has to use, however, is a baseball, a stopwatch, and a friend on the ground below with a long measuring tape. Bob is a pitcher, and knows that the fastest he can throw the ball is about 31.7 m/s. Bob starts the stopwatch as he throws the ball (with no way to measure the ball\'s initial trajectory), and...
Bob has just finished climbing a sheer cliff above a beach, and wants to figure out...
Bob has just finished climbing a sheer cliff above a beach, and wants to figure out how high he climbed. All he has to use, however, is a baseball, a stopwatch, and a friend on the ground below with a long measuring tape. Bob is a pitcher, and knows that the fastest he can throw the ball is about 33.7 m/s. Bob starts the stopwatch as he throws the ball (with no way to measure the ball\'s initial trajectory), and...
Bob has just finished climbing a sheer cliff above a beach, and wants to figure out...
Bob has just finished climbing a sheer cliff above a beach, and wants to figure out how high he climbed. All he has to use, however, is a baseball, a stopwatch, and a friend on the beach below with a long measuring tape. Bob is a pitcher and he knows that the fastest he can throw the ball is about ?0=31.7 m/s. Bob starts the stopwatch as he throws the ball (with no way to measure the ball's initial trajectory),...
Raskolnikov just finished a residence in internal medicine and wants to go into practice with Sophia...
Raskolnikov just finished a residence in internal medicine and wants to go into practice with Sophia and Katrina.Raskolnikov tells you that while he needs to practice with other physicians for call coverage and for other reasons, he does not want to be personally liable should the other physicians be found guilty of malpractice. You discuss various incorporation options with him, but he tells you that he would like to form a partnership. What business forms would you recommend to him...
Bob is a soccer player who has just scored the winning goal in the game. Bob,...
Bob is a soccer player who has just scored the winning goal in the game. Bob, who is also an observant physics student, noticed that when he received the pass, the soccer ball was moving 4.8 m/s 8° N of E and that after he kicked the ball it was moving at 25 m/s 41° E of S. What is the ball's change in velocity?
A consumer magazine wants to figure out which of two major airlines lost a higher proportion...
A consumer magazine wants to figure out which of two major airlines lost a higher proportion of luggage on international flights. The magazine surveyed Standard Air (population 1) and Down Under airlines (population 2). Standard Air lost 45 out of 600 bags. Down Under airlines lost 30 of 500 bags. Does Standard Air have a higher population proportion of lost bags on international flights? Which of the following is the appropriate conclusion at the 5% significance level?
Occupational Therapy of Your Area (OTYA) wants to figure out the average cost of three physical...
Occupational Therapy of Your Area (OTYA) wants to figure out the average cost of three physical therapy services. The practice uses a cost of $60 per RVU for its physical therapists, who are all contract workers paid by the relative value units they create. Physical therapy aides are paid $20/hr. They spend 15 minutes per service. The administrator of OTYA believes that RVUs are a solid way to reflect the cost of space, equipment use and administration. The total cost...
The figure shows a pendulum of length L = 2.6 m. Its bob (which effectively has...
The figure shows a pendulum of length L = 2.6 m. Its bob (which effectively has all the mass) has speed v0 when the cord makes an angle θ0 = 42° with the vertical. (a) What is the speed of the bob when it is in its lowest position if v0 = 9.1 m/s? What is the least value that v0 can have if the pendulum is to swing down and then up (b) to a horizontal position, and (c)...
The figure shows a pendulum of length L = 2.0 m. Its bob (which effectively has...
The figure shows a pendulum of length L = 2.0 m. Its bob (which effectively has all the mass) has speed v0 when the cord makes an angle θ0 = 32° with the vertical. (a) What is the speed of the bob when it is in its lowest position if v0 = 6.3 m/s? What is the least value that v0 can have if the pendulum is to swing down and then up (b) to a horizontal position, and (c)...
The figure shows a pendulum of length L = 2.6 m. Its bob (which effectively has...
The figure shows a pendulum of length L = 2.6 m. Its bob (which effectively has all the mass) has speed v0 when the cord makes an angle θ0 = 42° with the vertical. (a) What is the speed of the bob when it is in its lowest position if v0 = 9.1 m/s? What is the least value that v0 can have if the pendulum is to swing down and then up (b) to a horizontal position, and (c)...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT