# math

An object of mass 100g is thrown vertically upward from a point 60cm above the earths surface with an initial velocity of 150cm/sec. It rises briefly and then falls vertically to the earth, all of which time it is acted on by air resistance that is numerically equal to 200v (in dynes), where v is the velocity (in cm/sec).

a) find the velocity 0.1sec after the object is thrown.

b)find the velocity 0.1sec after the object stops rising and start falling.

1. 👍 0
2. 👎 0
3. 👁 390
1. net force=mass*acceleration
mg-200v=m*a
a=g-200v/mass

note we have a sign issue. if g is always downward, then if v is upowrd, then
a=g-200v/m
but when the motion is downward,
a=g+200v/m because v is now a negative sign....so on part b), one has to change the sign..

a) now we have an issue with calculus. One is tempted to use
vf=vi+at, however, a should be average acceleration, not the acceleration at t. However, because we are using very small time incrments, one can approximate the average a as the a at final time (similar to Simpson's right hand rule on incremental integration).
So as an approximation
vf=vi+at=150-(98+200v/100 )* .1
v=150-(98+.2v)
v(1.2)=52 calculate v

b. Same technique, however be mindful fo the sign for friction.

v(downward)=0-980-200v/100).1
v==98+.2v
v=-98/1.2 cm/sec

1. 👍 0
2. 👎 0
👨‍🏫
bobpursley
2. got this when i solve a)
ma = F
m dv/dt = -mg -kv

Putting in known quantities,

100 dv/dt = -100(980) - 200v
dv/dt = -980 - 2v
dv/dt + 2v = -980
v(0) = 150

1. 👍 0
2. 👎 0
3. IDK, TTYL, AF,BFF,SYl

1. 👍 0
2. 👎 0

## Similar Questions

1. ### science

a ball is thrown straight upward and returns to the thrower's hand after 3.00s in the air. A second ball is thrown at an angle of 30.0 deg with the horizontal. At what speed must the second ball be thrown so that it reached the

2. ### physics

two students are on a balcony 20.6 m above the street. One student throws a ball vertically downward at 14.7 m/s. At the same instant, the other student throws a ball vertically upward at the same speed. The second ball just

3. ### Algebra

THe function h(t)=-16t^2+v0t+h0 describes the height in feet above the ground h(t) of an object thrown vertically from a height of h0 feet, with an initial velocity of v0 feet per second, if there is no air friction and t is the

4. ### Physics

An object is thrown vertically and has an upward velocity of 18 m/s when it reaches one fourth of its maximum height above its launch point. What is the initial (launch) speed of the object?

1. ### physical science

A tennis ball is thrown vertically upward wih an initial velocity of 8.0m/s. A) What will its speed be wheen it returns to its tarting point? B) How long will it take for it to reach its starting poing?

2. ### physics

A ball is thrown vertically upward with an initial speed of 20 m/s. Two seconds later, a stone is thrown vertically (from the same initial height as the ball) with an initial speed of 24 m/s. At what height above the release point

3. ### physics

A hot-air balloon of mass 200 kg is descending vertically with downward acceleration of magnitude 1.2 m/s2. How much mass (ballast) must be thrown out to give the balloon an upward acceleration of magnitude 1.2 m/s2 (same

4. ### Physics

A research balloon of total mass 200 kg is descending vertically with a downward acceleration of 3.2 m/s^2. How much ballast must be thrown from the car to give the balloon an upward acceleration equal to 2.8 m/s^2, presuming that

1. ### Physics

A 2.83-kg object is thrown vertically upward from the surface of Mars, where the acceleration due to gravity is g1 = 3.71 m/s2. The initial velocity is v1, and the object reaches a maximum height of y1. What is the maximum height,

2. ### physics

An egg is thrown nearly vertically upward from a point near the cornice of a tall building. It just misses the cornice on the way down and passes a point 8.5 m below its starting point 3.0 s after it leaves the thrower’s hand.

3. ### Physics

I don't understand this at all! use the position equation s=-16t^2 +v0t+s0 to write a function that represents the situation. Find the average rate of change from t1 to t2. a) An object is thrown upward from a height of 6 feet at

4. ### Physics

An egg is thrown nearly vertically upward from a point near the cornice of a tall building. It just misses the cornice on the way down and passes a point a distance 37.0m below its starting point at a time 5.00 s after it leaves