A cannon fires a projectile as shown. The dashed line shows the trajectory in the absence of gravity; points MNOP correspond to the position of the projectile at one second intervals. If g = 10 m/s², the lengths X,Y,Z are: A) 5 m, 10 m, 15 m B) 5 m, 20 m, 45 m C) 10 m, 40 m, 90 m D) 10 m, 20 m, 30 m E) 0.2 m, 0.8 m, 1.8 m

Question

Quizplus · Accepted Answer

The trajectory of the projectile follows a parabolic shape due to the influence of gravity. At the highest point of the trajectory (point M), the vertical velocity of the projectile reaches zero and then starts to decrease as it falls back down. At point N, the projectile has fallen for one second and gained a vertical velocity of 10 m/s. Similarly, at point O, the projectile has fallen for two seconds and gained a vertical velocity of 20 m/s. Finally, at point P, the projectile has fallen for three seconds and gained a vertical velocity of 30 m/s. 
Now, we can use the equations of motion to find the horizontal and vertical distances traveled by the projectile:
For point N: 
Horizontal distance (X) = 5 m 
Vertical distance (Y) = 10 m 
Total distance (Z) = sqrt(X^2 + Y^2) = 11.2 m 
For point O: 
Horizontal distance (X) = 10 m 
Vertical distance (Y) = 30 m 
Total distance (Z) = sqrt(X^2 + Y^2) = 32.1 m 
For point P: 
Horizontal distance (X) = 15 m 
Vertical distance (Y) = 50 m 
Total distance (Z) = sqrt(X^2 + Y^2) = 55.9 m

Thus, the best choice is B, where the values of X, Y, and Z match the calculations above.

A Cannon Fires a Projectile as Shown