A body of mass 5kg is thrown vertically upwards.a air resistance of a constant retarding force 10N acting on the body .the ratio time of ascent and time of descent is .[use g=10m/s^2]

To solve this problem, we can use the equations of motion for vertical motion.

Step 1: Determine the acceleration of the body. Given that the acceleration due to gravity is g = 10 m/s^2, and there is a constant retarding force of 10 N acting on the body, we can calculate the net force acting on the body. Net force = Weight - Retarding force Weight = mass * acceleration due to gravity Weight = 5 kg * 10 m/s^2 = 50 N Net force = 50 N - 10 N = 40 N

Using Newton's second law, F = ma, we can find the acceleration: 40 N = 5 kg * a a = 40 N / 5 kg = 8 m/s^2

Step 2: Calculate the time of ascent. To find the time of ascent, we can use the equation of motion: v = u + at where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

At the highest point, the final velocity is 0 m/s (since the body momentarily stops before descending). The initial velocity can be found using the equation: v = u + at 0 m/s = u + (-8 m/s^2) * t u = 8 m/s * t

Now, we can use the equation of motion to find the time of ascent: 0 m/s = 8 m/s * t + (-8 m/s^2) * t^2 Rearranging the equation, we get: 8 m/s^2 * t^2 - 8 m/s * t = 0 t(8 m/s^2 * t - 8 m/s) = 0

This equation has two solutions: t = 0 (which corresponds to the initial time) and t = 1 s (which corresponds to the time of ascent).

Step 3: Calculate the time of descent. Since the time of ascent is 1 s, the total time of flight (time of ascent + time of descent) is 2 s. Therefore, the time of descent is: Time of descent = Total time of flight - Time of ascent Time of descent = 2 s - 1 s = 1 s

Step 4: Calculate the ratio of time of ascent to time of descent. The ratio of time of ascent to time of descent is given by: Ratio = Time of ascent / Time of descent Ratio = 1 s / 1 s = 1

Therefore, the ratio of time of ascent to time of descent is 1.