Question

While riding your bike at 10 m/s, you hit a bump causing your calculator to fall out of your backpack from a height of 1.5 m. How far is the calculator from the bump once it hits the ground?

a) 3.75 meters
b) 5 meters
c) 15 meters
d) 19.5 meters

Answer 1

The calculator will be approximately 5 meters from the bump when it hits the ground, based on the horizontal velocity and the time calculated from the vertical motion equation.

Step-by-step explanation:

To determine how far the calculator is from the bump once it hits the ground, we need to consider both horizontal and vertical motions separately because this is a projectile motion problem. The calculator's horizontal velocity (10 m/s) does not change because horizontal motion is not affected by gravity. To find the time it takes for the calculator to hit the ground, we use the formula for vertical motion under constant acceleration due to gravity (g=9.81 m/s2):

h = (1/2)gt2

With the height (h) as 1.5 m, we can solve for the time (t):

1.5 = (1/2)(9.81)t2

t2 = 1.5 / (1/2)(9.81)

t2 = 1.5 / 4.905

t2 = 0.3058

t ≈ √0.3058

t ≈ 0.553 s

Now we can find the horizontal distance travelled as:

distance = velocity × time

distance = 10 m/s × 0.553 s

distance ≈ 5.53 m

However, since the options given do not include this exact result, the closest answer we can choose is:

b) 5 meters