A simple pendulum and a mass hanging on a spring both have a period of 1$ when set into small oscillatory
motion on Earth. They are taken to Planet X, which has a larger acceleration due to gravity. Which of the
following statements is true about the periods of the two objects on Planet X compared to their periods on Earth
a. Both are shorter
b. Both are the same
e. Both are longer
d. The period pf the mass on the spring is shorter, that of the pendulum is the same
e. The period of the pendulum is shorter, that of the mass on the spring is the same,

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?