An object is projected with velocity 10 m/s at angle 45° with the horizontal. The velocity of this object when its direction becomes perpendicular to velocity of projection, is_____m/s.
Answers
Step-by-step explanation:
Method 1: Using properties of projectile motion
As we have to calculate the time between two positions A and B where the final direction of movement is perpendicular to the initial direction of movement. So for our own comfortability, we can choose the initial direction of motion as x-axis. Also let us assume the velocity at position B to be v.
Now analyzing motion in x-and y-direction, we have
ux=u; uy=0
ax=−gsinθ;ay=−gcosθ
Here we can use the following formula v=u+ at in x-direction. As we have the values of initial velocity, final velocity, and acceleration we can find t. Therefore,
vx=ux+axt
At position B, vx=0, as the final velocity is equal to the y-component of velocity. Therefore,
0=u−gsinθ.t
Thus, t=gsinθu which is the required time to travel.
Method 2: Using vectors
As u and v both are perpendicular to each other. We can use the orthogonality property of dot product, i.e., if two vectors are perpendicular to each other their dot product is zero, in order to find out the time of travel to the desired position. So,
So, u.v=0⇒u.(u+at)=0⇒u.u+u.at=0
⇒u2+ugcos(90o+θ)t=0
[Because angle between u and g is 90o+