11 An aeroplane is travelling horizontally at a speed of 80 ms", and drops a crate of emergency supplies (Figure 2.39). To avoid damage, the maximum vertical speed of the crate on landing is 20 ms.
You may assume air resistance is negligible.
80 ms
Figure 2.39 For End-of-chapter Question 11.
a Calculate the maximum height of the aeroplane when the crate is dropped.
b Calculate the time taken for the crate to reach the ground from this height.
• The aeroplane is travelling at the maximum permitted height Calculate the horizontal distance travelled
by the crate after it is released from the aeroplane.
12
12

0.11 m/s and 0.28 m/s should be correct

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.