Chapter A.8, Problem 37AYU

To determine

To find: What yard line will the defensive back catch up to the tight end?

Answer to Problem 37AYU

The defensive back catches up to the tight end the 45 yard line in 3 sec.

Explanation of Solution

Given:

A tight end can run the 100-yard dash in 12 seconds. A defensive back can do it in 10 seconds. The tight end catches a pass at his own 20-yard line with the defensive back at the 15-yard line. If no other players are nearby.

Calculation:

For the tight end: $d_t=r_t.t_t$.

For the defensive back: $d_d=r_d.t_d$.

Given: $r_t=\frac{100}{12}\text{yards/sec}$, $r_d=\frac{100}{10}\text{yards/sec}$.

The times are same since they will run for the same amount of time call both times.

$d_t=d_d-5$ yards

$d_t=r_t.t_t$

$d_d-5=\frac{100}{12}.t$

$d_d=\frac{100}{10}.t$

Therefore $t=3$ sec.

$d_t=\frac{100}{12}\cdot 3=25$ yards.

$d_d=\frac{100}{10}\cdot 3=30$ yards.

The tight end runs from his 20 yards line for 25 yards and gets to the 45 yards line in 3 sec.

The defensive back runs his 15 yard line for 30 yards and gets to the 45 yard line in 3 sec.