A tiger can run at approximately 100 km/hr (27.7 m/s) and a zebra at 80 km/hr (22.2 m/s). If both animals are running at full speed, with the zebra 70.0 m ahead, how long before the tiger catches its prey?
a) 12.6 s
b) 25.2 s
c) 6.30 s
d) 10.7 s
To find out how long it will take for the tiger to catch its prey, we can use the equation of motion:
distance = speed × time
Let's assume that it will take time t for the tiger to catch the zebra.
The distance both animals will travel during this time can be expressed as follows:
Distance traveled by tiger = t × 27.7 m/s
Distance traveled by zebra = t × 22.2 m/s + 70.0 m
Since both animals will cover the same distance when the tiger catches the zebra, we can set up an equation:
t × 27.7 = t × 22.2 + 70.0
Now, let's solve for t:
27.7t = 22.2t + 70.0
27.7t - 22.2t = 70.0
5.5t = 70.0
t = 70.0 / 5.5
t ≈ 12.73s
Therefore, it will take approximately 12.73 seconds for the tiger to catch its prey.
The closest option is "b) 25.2 s." However, this is not the correct answer.
To find the time it takes for the tiger to catch the zebra, we can use the formula:
time = distance / relative speed
First, let's find the relative speed between the tiger and the zebra. The relative speed is the difference in their speeds:
relative speed = speed of the tiger - speed of the zebra
= 27.7 m/s - 22.2 m/s
= 5.5 m/s
Now we can calculate the time it takes for the tiger to catch the zebra:
time = distance / relative speed
= 70.0 m / 5.5 m/s
≈ 12.7 s
So the closest option is 12.6 seconds (option a).