A ball is thrown with a velocity of 15 ./sec at a angle of 30° with the horizontal. Find out the time of floght nd maximum height. (G = 10m /sec)
Answers
If we take the usual easy-out of no air drag, then using the splendid physics student’s method of working the horizontal and vertical axes separately, we soon realize that the total time of flight is controlled by the vertical axis: so when the ball descends to the starting height, the game is over!
The only other trick needed is elementary trigonometry. The vertical speed is the vertical side of a triangle, whose diagonal represents the velocity of 15 m/s, using the formula for the sine ratio, which is vertical divided by diagonal. So we calculate the length of the vertical (representing the vertical speed) in this way:
sine 30 deg = (vertical / diagonal)
= (vertical speed / 15)
so vertical speed = 15*sin(30)
= 15*0.5 = 7.5 m/s
Now we chose the applicable equation from the four main kinematic equations:
We know the initial vertical velocity, we can easily see that the constant acceleration (g) reduces the velocity equally over time and so the ball lands with the same speed it started - in the other direction!
V final = V initial + a*t will work for us if we visualize the trajectory carefully; using up is positive and g is negative we get -7.5 = 7.5 -10*t which simplifies to 10*t = 15 and t = 1.5 seconds.