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raketka [301]
3 years ago
12

The tortoise and the hare are having a race over a course of length 0.52 km. The tortoise crawls along at a constant 0.075 m/s w

hile the hare sprints along at a constant 16.7 m/s (when he is not sleeping). The race starts and the hare runs halfway to the finish line and decides to take a nap while the tortoise plods along. Waking from his nap, the hare sees that the tortoise has made so much progress that he might lose the race. He takes off and just catches up to the toroise at the finish line so that the race ends in a tie. Be careful with units.
How many hours did the hare sleep before waking up?
Physics
1 answer:
EastWind [94]3 years ago
3 0

Answer:the hare slept for 1 hr 55minutes.

Explanation: distance is changed to meters = 520m

Speed=distance/time

Speed of tortoise is 0.075m/s=520m/t

Crops multiplying t= 520/0.075 = 6933.3 seconds.

Speed for hare 16.7m/s =260m/t

ie 260m is half of the distance.

t =15.56seconds

Therefore the time slept by the hare = 6933.3- 15.56= 6917.74 seconds.

Converting to hours = 1hr. 55minutes is the time the hare slept.

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A hovering mosquito is hit by a raindrop that is 50 times as massive and falling at 8.4 m/s, a typical raindrop speed. How fast
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The final velocity after the collision is 8.2 m/s

Explanation:

We can solve this problem by using the law of conservation of momentum: in fact, if we consider the system to be isolated (=no external unbalanced forces), the total momentum of the raindrop+mosquito must be conserved before and after the collision.

If the collision is perfectly inelastic, moreover, the raindrop and the mosquito stick together and travel at the same velocity v after the collision.

Mathematically:

p_i = p_f\\m_1 u_1 + m_2 u_2 = (m_1+m_2)v  

where:  

m_1 is the mass of the first mosquito

u_1 = 0 is the initial velocity of the mosquito

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v is the final combined velocity of the raindrop+mosquito

Re-arranging the equation and substituting, we find:  

m_1 u_1 + 50 m_1 u_2 = (m_1 + 50 m_1) v\\50 m_1 u_2 = 51 m_1 v\\50 u_2 = 51 v\\v=\frac{50}{51}u_2 = \frac{50}{51}(8.4)=8.2 m/s

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