Hi, can you please help me answer these following questions?

1. You have won another space trip. This time you will be travelling at a constant speed of 2.90 x 10^8 m/s relative to earth. Now your best friend had to stay behind on earth. Your friend aged 25 years during the time of your trip. How many years did you age?

2.Now your friend is travelling at a velocity of 0.80 c towards you. You arestationary on earth. Your friend throws a baseball forward at a velocity of 0.60 c(relative to your friend). What is the velocity of the baseball with respect to you?

3. The mass of beryllium nucleus (7, 4 Be) is 1.1652 x 10^-26kg. What is the mass defect of the beryllium nucleus? What is the binding energy of the beryllium nucleus? What is the binding energy per nucleon on the beryllium nucleus?

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1. You need to use the relativistic time dialation formula:

`t = t_0/sqrt(1 - v^2/c^2)` , where `t_0` is the time elapsed in Earth reference system, 25 years, *v *is the speed you have traveled with, `2.9 * 10^8 m/s` , and *c* is the speed of light, `3* 10*8 m/s` .

Thus, the time that elapsed in your reference system, and this is how much you aged, is

`t = 25/sqrt(1 - 2.9/3)=136.9` years

**The answer is 136.9 years.**

2. You need to use the formula for the addition of relativistic speeds:

`v=(v_0+u)/(1+(v_0*u)/c^2)` . where *u* is the speed of the reference system that is moving (your friend), `v_0` is the speed of the baseball in the moving system (your friend) and *v *is the speed of the baseball in the stationary system (you). And, *c* is again the speed of light.

Plugging in *u* = .8*c* and `v_0 = .6c` you get

`v=(.8c+.6c)/(1+(.8*.6c^2)/c^2)=(1.4c)/1.48=35/37c`

**The velocity of the baseball with respect to you is ** `35/37 c` .

**Sources:**

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