A rectangular box of height h metres with a square base with side x(t) metres, where initial leng...
I'm not sure about b,c,d. Is there anyone can help with this question? A rectangular box of height h metres with a square base with side x(t) metres, where initial length of the side of the base is x(0) 2 metres. The box is initially filled with water to a height of h(0)4 metres. The volume of water is given by Vt)(t) Over time, the sides of the base are decreasing ata ateof0.05 m/s and the water is leaking from...
I only want the answer for No 2 Note: The time it takes to get a two-liter bottle empty is given in the picture I only want the answer for No 2 Let h(t) and V(t) be the height and volume of water in a tank at time t. If water drains through a hole with area a at the bottom of the tank, then Torricelli's Law says that dV dt where g is the acceleration due to gravity. So...
the height , h(t) in metres of the trajectory of a football is given by h(t) = 2+28t-4.9t^2, where t is the time in flight, in seconds . Determine the maximum height of thefootball and the time wehn the height is reached
5. A pebble falls from the top of a cliff that is 180 m high. The pebble's height above the ground is modelled by h(t) -5t-5t+180 where h is the height in metres at t seconds since the pebble started to fall. a. Find the average rate of change between 1 s and 4 s. b. Find h(3) c. Find the instantaneous rate of change of height at 3 s. d. Explain the meaning of each value calculated in parts...
The height, h, in metres, above the ground of a rider on a Ferris wheel can be modelled by the equation:h= 10 sin ((pi/15 t) - 7.5) + 12 where t is the time, in seconds.At t=0, the rider is at the lowest point. Determine the first two times that the rider is 20 m above the ground, to the nearest hundredth of a second.
1. Civil engineers use the continuity equation for many applications. This simple ordinary differential equation states that the difference between (volumetric) rates of inflow and outflow is equal to the rate of change of storage in the system: I- o- dS/dt where S is storage or volume and t is time Consider a conical tank with top radius, r-1.83 meters and height, h- 3.05 meters. Thetank is initially empty, and then water is added at a rate of I- 0.00095...
12. During the first 30seconds of its flight, a test rocket's height in metres above its launching point is given by h(t) = 452 – where t is the elapsed time in seconds. (a) Find an equation for the velocity of the rocket and use this to find how long it will take to reach 600m/s. (b) What height will the rocket be at this time? 13. Draw the graphs of the functions in question 12 in the same coordinate...
1. An airplane if flying horizontally at a constant height of 6 km above a fixed observation point. At a certain moment the angle of elevation θ is 30° and decreasing and the speed of the plane is 4 km/h. (a) How fast is 0 decreasing at this moment? (b) How fast is the distance between the plane and the observation point is changing at this moment? 2. Trajectory of a particle is described by parametrical equations as t,y P,...
A barge floating in fresh water (p=1000 kg/m3) is shaped like a hollow rectangular prism with base area A=450 m2 and height H=2.0 m. When empty the bottom of the barge is located H0=0.55 m below the surface of the water. When fully loaded with coal the bottom of the barge is located H1 = 1.4 m below the surfacePart (a) Find the mass of the coal in kilograms. Part (b) How far would the barge be submerged (in meters) if...
Problem 4 4.50 A conical flask contains water to height H=36.8 mm, where the flask diameter is D = 29.4 mm. Water drains out through a smoothly rounded hole of diameter d= 7.35 mm at the apex of the cone. The flow speed at the exit is approxi- mately V = V2gy, where y is the height of the liquid free surface above the hole. A stream of water flows into the top of the flask at constant volume flow...