Question

In: Math

A stone is thrown upward on the moon with its height (in feet) after t seconds...

A stone is thrown upward on the moon with its height (in feet) after t seconds given by h(t) = 20 − 5t2. Include units with your answer.

a) What is the acceleration of the stone at 2 seconds?

b) What is the average velocity of the stone between 1 and 3 seconds?

c) What is the instantaneous velocity of the stone at 2 seconds?

d) With what velocity does the stone hit the ground?

Solutions

Expert Solution

Note: I think there might be a mistake in the question as the height function implies to initial velocity, but the question mentions that the stone is thrown upward.

Still, I have done whatever the question asked me to do


Related Solutions

A rock is thrown upward from a bridge that is 83 feet above a road. The rock reaches its maximum height above the road 0.61 seconds after it is thrown and contacts the road 3.87 seconds after it was thrown.
  A rock is thrown upward from a bridge that is 83 feet above a road. The rock reaches its maximum height above the road 0.61 seconds after it is thrown and contacts the road 3.87 seconds after it was thrown. Write a function f that determines the rock's height above the road (in feet) in terms of the number of seconds tt since the rock was thrown. THE FUNCTION MUST BE IN THE FORMAT f(t)=c⋅(t−t_1)(t−t_2) for fixed numbers c,...
Assume that the height of a ball in feet off of the ground after t seconds...
Assume that the height of a ball in feet off of the ground after t seconds is given by the function h(t). If you know the following about the function h and its derivative 1. h(5) = 250 ft 2. h'(1) = 15 ft/sec 3. h'(5) = 0 ft/sec 4. h'(6) = -2 ft/sec Recall that h'(t) is the derivative of h at seconds, and h(t) is the function h evaluated at t seconds. Explain what each of the 4...
1. A stone is thrown upward from a tower with initial velocity of 3 m/s. Height...
1. A stone is thrown upward from a tower with initial velocity of 3 m/s. Height of tower is 50 m above the ground. What would be its position after 3.4 secs? What would be its speed after 3.4 secs? What would its velocity be when it hits the ground? 2. Duterte throws a ball upward at 15 m/s while standing on the edge of a building so that the ball can fall to the base of the building 50...
A stone is thrown vertically upward at a speed of 48.00 m/s at time t=0. A...
A stone is thrown vertically upward at a speed of 48.00 m/s at time t=0. A second stone is thrown upward with the same speed 4.050 seconds later. At what time are the two stones at the same height? Set up an equation of motion for each stone. Write the time for the second stone in terms of the time for the first stone. Solve the two equations for the unknown time.
s(t)= 5t + 3/t^2  be the position in feet of a particle after t seconds for t...
s(t)= 5t + 3/t^2  be the position in feet of a particle after t seconds for t ≥ 1. (a) Compute the average velocity from t = 1 to t = 3. Include units in your answer (b) Where is the velocity = 0? (c) Show the accelaration for t ≥ 1 is positive. (d) What are the units for the acceleration?
Suppose a ball has a maximum height of 24 feet after 11 seconds of travel. This...
Suppose a ball has a maximum height of 24 feet after 11 seconds of travel. This same ball will have a height of 8 feet after 20 seconds of travel. Find Upper H left parenthesis Upper T right parenthesis equals AT squared plus BT plus Upper C commaH(T)=AT2+BT+C, where​ H(T) is the height of the ball in inches after T seconds. Answers in Exact Form.
A rock is thrown upward from a bridge that is 31 feet above a road. The...
A rock is thrown upward from a bridge that is 31 feet above a road. The rock reaches its maximum height above the road 0.57 seconds after it is thrown and contacts the road 2.53 seconds after it was thrown. Write a function ff that determines the rock's height above the road (in feet) in terms of the number of seconds tt since the rock was thrown. f(t)=
A rock is thrown upward from a bridge that is 59 feet above a road. The...
A rock is thrown upward from a bridge that is 59 feet above a road. The rock reaches its maximum height above the road 0.9 seconds after it is thrown and contacts the road 2.4 seconds after it was thrown. Write a function f that determines the rock's height above the road (in feet) in terms of the number of seconds t since the rock was thrown. f(t)=    Hint: the function f can be written in the form f(t)=c⋅(t−t1)(t−t2) for...
A ball is thrown vertically upward from the top of a building 112 feet tall with...
A ball is thrown vertically upward from the top of a building 112 feet tall with an initial velocity of 96 feet per second. The distance s  (in feet) of the ball from the ground after t seconds is s (t) = 112 + 96t - 16t2 Complete the table and discuss the interpretation of each point. t s(t) Interpretation 0 0.5 1 2 100 100 200 200 Answer these questions. After how many seconds does the ball strike the...
A stone is thrown vertically upward with an initial velocity of 20 m/s. Air resistance is...
A stone is thrown vertically upward with an initial velocity of 20 m/s. Air resistance is considered negligible. (1) At what time does it reach the peak? (2) What is the maximum height it reaches? (3) What is speed of the stone just before it hits the ground? The velocity of a 1-kg particle moving along the x axis changes from vi = -2m/s to vf = -5m/s in 3s. (1) What are the change in momentum and impulse for...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT