Question

Batman drops his keys off a building that is 100 m tall, and they fall straight down.

He throws his grappling hook straight down 1 second after the keys fall to try to catch
them. The initial velocity of the keys is 0 m/s and the initial velocity of the grappling
hook is 10 m/s. When does the grappling hook catch the keys? (Assume that the
grappling hook is a simple projectile)

(a) Not before the keys hit the ground
(b) 5 m above the ground
(c) 35 m above the ground
(d) 10 m above the ground
(e) 25 m above the ground

Answer 1

(a) Not before the keys hit the ground

Step-by-step explanation:

1 second after being dropped:

---> y = 1/2gt^2

----> y = 1/2 * 9.8 * 1 = 4.9 m

Speed of the keys after 1 second:

----> v = vi + at

----> v = 0 + 9.8 * 1 = 9.8 m/s

Relative speed of drop with respect to key:

---> vr = 10 - 9.8 = 0.2 m/s

time taken by the drop to cover the distance between them

---> d = vr * t

---> 4.9 = 0.2 * t

---> t = 24.5 s

during this time, the key will drop to the position:

---> y = 1/2gt^2

---> y = 1/2 * 9.8 * 25.5^2

---> y = 3186.22 m

Due to it being larger than the building, none of the keys will result in hitting the ground when the grappling hook catches it hypothetically.

Thank you,

Eddie