a) The pencil takes approximately 0.37 seconds to reach the floor. b) During this time, the pencil travels approximately 0.74 meters horizontally.
a) To calculate how long it takes for the pencil to reach the floor, we can use the equation for free fall motion: h(t) = h0 + v0t + (1/2)gt^2. Since the pencil is dropped horizontally, the initial vertical velocity is 0. The initial height h0 is 65 cm and the acceleration due to gravity g is 9.8 m/s^2. Plugging in these values, we get:
0 = 0 + (1/2)(9.8)t^2
Simplifying the equation, we find that t = √(2h0/g). Substituting the values, we get:
t = √(2(0.65)/9.8) ≈ 0.37 seconds
b) To calculate the horizontal distance traveled by the pencil, we can use the equation for constant velocity motion: d = v0t. Since the pencil is dropped horizontally, the initial velocity v0 is 2.0 m/s and the time t is 0.37 seconds. Plugging these values, we get:
d = 2.0 × 0.37 ≈ 0.74 meters