A body is thrown at an angle `theta_0` with the horizontal such that it attains a speed equal to `(sqrt((2)/(3))` times the speed of projection when the body is at half of its maximum height. Find the angle `theta_0`.

A body is thrown at an angle `theta_0` with the horizontal such that i

1.	A body is thrown at an angle `theta_0` with the horizontal such that it attains a speed equal to `(sqrt((2)/(3))` times the speed of projection when the body is at half of its maximum height. Find the angle `theta_0`.
Answer» At any height `y`, the speed of the projectile is `v = sqrt(v_0^2 - 2 g y))`, where `y = (y_(max))/(2)` Sunstituting `y_(max) = (v_0^2 sin^2 theta_0)/(2 g)`, we have `v = v_0 (sqrt(1 - (sin^2 theta_0)/(2)))` Since `v = sqrt((2)/(3)) v_0` (given), we have `1 -(sin^2 theta_0)/(2) = (2)/(3)` This given `sin theta_0 = sqrt((2)/(3))`. Hence, `theta_0 = sin^-1 (sqrt((2)/(3)))`.

Discussion

No Comment Found

Related InterviewSolutions

From the top of at all building (height27.3m), a boy throws an apple upward, which strikes ground after 16 s. Take `g = 9.8 m//s^(2)`, find the speed of apple with which it was thrown and the maxium height reached by it.
A car travels along a straight line for first half time with speed `40 km//h` and the second half time with speed `60 km//h`. Find the average speed of the car.
A vechicle travels along a straight path between two places `alpha and beta`. It travels first half of the distance with a velocity of 72 km `h^(-1)` and the remaining distance with a velocity of 36 km `h^(-1)` then the average velocity of the vehicle is ______ m`s^(-1)` A. 11.3B. 13.3C. 15D. 14
In the case of a simple pendulum, a graph is drawn between the displacement and time taken for its oscillations as shown in the figure . Then From the given figure, the number of oscillation performed by the bob at the end of 21 s is ________ A. 3B. 4C. 2D. `3^(1//2)`
`{:("ColumnA","ColumnB"),(A. "Periodic motion",a."maximum displacement of vibrating particle from its mean position"),(B."Vibrtory motion" ,b."The pistion of a motor car engine at uniform car engine at uniform speed"),(C."Body at rest" ,c."Non- uniform motion"),(D."Amplitude",d.18//5 kmh^(-1)),(E."Variable speed" ,e."OScillating objects undergo change in shape of size"),(F. 1ms^(-1) , f. ("Total displacement")/("Total time")),(G."Average velocity" ,g. "Zero velocity"):}`
`{:( "Column A"," ColumnB"),(A. "Non- uniform motion","a. To measure speed of the vehicle"),(B."Oscillatory motion","b. Uniform motion"),(C."Mean position" , "c. A criket ball that rolls over ground"),(D."Speedometer","d.The needle of sewing machine that moves up and down"),(E."Constant speed","e. Freely suspended pendulum at rest"),(F. "Acceleration","f".("Total change in velocity")/("Total time taken for change")):}`
`{:( "Column A"," ColumnB"),(A."Speed",a."Uniform motion"),(B."Time",b."Non-uniform motion"),(C."Average speed",c."km h"^(-1)),(D."Uniform speed in a straight line",d."second"),("E. Freely falling body","e. Change in time period"),("F. Change in length of a pendulum","f".("Total distance")/("Total time")):}`
`{:("Column A" ,"ColumnB"),((A)"A body covers 5 m in every subsequent second",(a)"Lunar month"),((B)"Equal distances in unequal intervals of time",(b)"Non-uniform speed"),((C) "Periodic motion of the moon around the earth",(c)"Years"),((D)"Approprite unit to express the age of a person",(d) "Constant speed"):}`A. `A to b, B to c, C to d,D to a `B. `A to d, B to b, C to a, D to c`C. `A to d, B to a, C to b, D to c`D. ` A to a, B to b, C to c, D to d`
A ball thrown by one player reaches the other in `2 s`. The maximum height attained by the ball above the point of projection will be about.A. 2.5 mB. 5 mC. 7.5 mD. 10 m
A thief in a stolen car passes through a police check post at his top speed of `90 kmh^-1.` A motorcycle cop, reacting after 2 s, accelerates from rest at `5 ms^-2.` His top speed being `108 kmh^-1.` Find the maximum separation between policemen and thief.A. `112.5 m`B. `115 m` (c) 116.5 m (1) None of theseC. `116.5 m`D. None of these

A body is thrown at an angle `theta_0` with the horizontal such that it attains a speed equal to `(sqrt((2)/(3))` times the speed of projection when the body is at half of its maximum height. Find the angle `theta_0`.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment