- #1

Beth N

- 41

- 4

## Homework Statement

Problem: 5. 37 [/B]

With reference to the figure below, the projectile is fired with an initial velocity ##v_0=35 m/s ## at θ=23°.

Truck is moving along X with constant speed of 15m/s

At instant projectile is fired, back of truck is at x=45m

Find time for the projectile to strike back of the truck if the truck is very tall.

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## Homework Equations

##x=x_0+v_0t+(\frac 1 2)at^2##

##v_{ave}=Δx/Δt ##

##v_x=vcosθ ## ; ##v_y=vsinθ ##

## The Attempt at a Solution

At first I thought that I can assume that the project tile hits the truck right at the position where y=0. My equation was:

##y-y_0=v_{0y}t+(\frac 1 2)at^2=0 ##

##t= \frac {-v_{0y} *2} {a} ##

##t= \frac {-35sin(23)*2} {-9.8} ##

##t=2.79 ##

The key is 2.614, which is less than 2.79, which means the projectile strikes the truck before it reaches the ground. The time it takes for the projectile to land the ground (and complete the curve) is greater than the time it takes to hit the truck, as the diagram indicate.

**My 1st question: How can I be sure that it is so? What does the key mean by saying "at the moment of overtaking it"**? I was stuck on the way I formulate an equation for the time, which was this.

## t_{time taken to strike truck}=t_{time taken for Δy=0} - t_{?? not sure how to determine} ##

It seems like I have an ineffective way of thinking through this problem, and I'm curious on what are better ways.

Unfortunately, it took me a long time (20 minutes for this one) to brainstorm the solution even though on tests I'm supposed to solve them in 3-5 minutes. I understand the concept of projectile motion, but cannot apply to problems. How can I be faster? I tried several methods including re-drawing the diagrams and putting variables in a table like below.

**My 2nd question : how to improve in general problem-solving in physics, specifically problems about kinematics. Thank you!**