A small cannonball with mass 4 kilograms is shot vertically upward with an initial velocity of 190 meters per second. If the air resistance is assumed to be directly proportional to the speed of the cannonball, a differential equation modeling the projectile velocity is dv m = mg mg - kv dt Assume that k = 0.0025, and use g = -9.8 meters/second². Solve the differential equation for the velocity v(t). Don't forget to include the initial condition. v(t) = = Integrate the velocity to obtain the height h(t) as a function of time. Assume the cannonball is launched from ground level at t = 0. h(t) = Find the maximum height reached by the cannonball. Max height = meters

Let y(t) be the height (in meters) after time t (in seconds) of a rover that is landing on some other planet with the help of a parachute. Taking into account gravity and air resistance, physicists suggest that the air resistance is proportional to velocity. Further data suggests that the fall can be modeled by y"=-4-3y'. If the parachute is released at a height of 600m with an initial velocity of 0m/s, what is its height after t seconds? What is its terminal velocity? y(t) = The terminal velocity is m/s. m/s

Let y(t) be the height (in meters) after time t (in seconds) of a rover that is landing on some other planet with the help of a parachute. Taking into account gravity and air resistance, physicists suggest that the air resistance is proportional to velocity. Further data suggests that the fall can be modeled by y"=-5-3y'. If the parachute is released at a height of 600m with an initial velocity of 0m/s, what is its height after t seconds? What is its terminal velocity? y(t) = The terminal velocity is Submit m/s. m/s

العنوان оне hot small copper ball [c in kJ/kg.°C, k in W/m.°C] is suddenly placed in water maintained at 100 °C. The convection heat transfer coefficient is h in W/m². ºC. Derive equation to calculate the time required to reduce ball to temperature T.

The solution for t of the equation e^t=x is A. t= x/e B. t=lnx-1ne C. t=1nx D. t=1nx/e

A A particular organism reproduces at a rate of f(t) = 22 population starts with 175 organisms, then how many c

Let y(t) be the height (in meters) after time t (in seconds) of a rover that is landing on some other planet with the help of a parachute. Taking into account gravity and air resistance, physicists suggest that the air resistance is proportional to velocity. Further data suggests that the fall can be modeled by y"=-4-3y'. If the parachute is released at a height of 600m with an initial velocity of 0m/s, what is its height after t seconds? What is its terminal velocity? y(t) The terminal velocity is m/s. m/s